geometry assignment find the measure of angle b

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Measuring angles

Here you will learn about measuring angles, including how to measure an angle using a protractor.

Students first learn about measuring angles as part of geometry in 4 th grade. They expand that knowledge as they progress through middle school and high school.

What is measuring angles?

Measuring angles is finding the number of degrees an angle is. Angles are measured in degrees using the degree sign ^{\circ} . The tool used for measuring angles is called a protractor .

The degree measure on the top center of a protractor is 90^{\circ} . This is the midpoint of the protractor. Note that the numbers to the left and to the right of the center either go up by ten or go down by ten degrees.

If the angle is acute, you will use the acute measurement (less than 90^{\circ} but greater than 0^{\circ} ), and if the angle is obtuse, you will use the obtuse measurement (greater than 90^{\circ} but less than 180^{\circ} ).

For example, let’s look at the measure of ∠D.

The vertex of the angle, D , is placed on the bottom center of the protractor. One arm of the angle is lined up with the bottom of the protractor at 0^{\circ} . The other arm is used to measure the turn from one arm to the next.

Notice how the arm goes through the measure of 40^{\circ} and 140^{\circ} . Since the angle is obtuse, use the measurement that is greater than 90^{\circ} and less than 180^{\circ} . The angle measure 140^{\circ} .

The angle on a protractor may not always line up with the bottom of the protractor at zero. If this happens, you will subtract in order to find the measurement of the angle.

For example, let’s look at the measure of ∠abc.

Notice how both point A and C are on an angle measure greater than zero. You will have to subtract in order to find the measure of the angle. In order to calculate the correct measure, decide whether to use the top angle measurements or bottom angle measurements.

If using the top angle measurements, notice the arms of the angles read 150^{\circ} and 40^{\circ} . If using the bottom angle measurements, notice the arms of the angles read 140^{\circ} and 30^{\circ} .

To find the measure of the angle, you will subtract the two angle measurements.

150-40=110^{\circ}

140-30=110^{\circ}

The measure of the angle is 110^{\circ} .

[FREE] Angles Check for Understanding Quiz (Grade 4)

Use this quiz to check your grade 4 students’ understanding of angles. 10+ questions with answers covering a range of 4th grade angles topics to identify areas of strength and support!

Common Core State Standards

How does this apply to 4 th grade math and 7 th grade math?

• Grade 4 – Measurement and Data (4.MD.C.6) Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.
• Grade 4 – Measurement and Data (4.MD.C.7) Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, example, by using an equation with a symbol for the unknown angle measure.
• Grade 7 – Geometry (7.G.B.5) Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.

How to measure angles

In order to measure an angle, you need to:

Determine the type of angle.

Check to make sure the vertex is at the center of the protractor and one side of the angle is lined up with the bottom of the protractor.

Find the degree measure.

Measuring angle examples

Example 1: arm of angle is lined up with zero.

Find the measure of the given angle.

The angle is an acute angle because it appears to be less than 90^{\circ} .

2 Check to make sure the vertex is at the center of the protractor and one side of the angle is lined up with the bottom of the protractor.

The vertex is placed correctly on the protractor. The arm is lined up correctly on the bottom of the protractor.

3 Find the degree measure.

The other arm goes through the 70^{\circ} and 110^{\circ} . Since the angle is acute, the correct measure is 70^{\circ} .

Example 2: arm of angle is lined up with zero

The angle is an obtuse angle because it appears to be greater than 90^{\circ} .

The other arm goes through the 40^{\circ} and 140^{\circ} . Since the angle is obtuse, the correct measure is 140^{\circ} .

Example 3: arm of angle is lined up with zero

The other arm goes through the 75^{\circ} and 105^{\circ} . Since the angle is obtuse, the correct measure is 105^{\circ} .

How to measure angles that are not aligned at zero

In order to measure an angle that is not aligned at zero, you need to:

After deciding which degree measures to use, find the degree measure for each arm.

Subtract the degree measures.

State the number of degrees measured.

Example 4: arm of angle is not lined up with zero

Angle ABC is an obtuse angle because it appears to be greater than 90^{\circ} .

Using the measures that run from left to right, the arm at point A goes through 25^{\circ} , and the arm at point C goes through 160^{\circ} .

Subtract the two measures,

The measure of angle ABC is 135^{\circ} .

Example 5: arm of angle is not lined up with zero

Using the measures that run from left to right, the arm at point A goes through 45^{\circ} , and the arm at point C goes through 90^{\circ} .

State the number of degrees measured

The measure of angle ABC is 45^{\circ} .

Example 6: arm of angle is not lined up with zero

Using the measures that run from left to right, the arm at point A goes through 33^{\circ} , and the arm at point C goes through 119^{\circ} .

The measure of angle ABC is 86^{\circ} .

Teaching tips for measuring angles

• Introduce the protractor by allowing students to use and investigate the tool. Make sure students are comfortable with the different parts of the protractor including the straight edge, the curved edge with degree markings and the midpoint.
• Before jumping into measuring, make sure students are able to identify the different types of angles: acute angle, obtuse angle, right angle, straight angle, and reflex angle.
• While angle worksheets have their place when working with measuring angles, allowing students to have real-world practice using protractors in the classroom is important. Allow students to draw angles and practice measuring the angle using a protractor.

Easy mistakes to make

• Reading the wrong scale when measuring angles A protractor has two different sets of degree markings at the top, one that reads from left to right, and one that reads from right to left. Make sure you have identified the type of angle (acute or obtuse) before deciding which angle markings to read from.

Related angles lessons

• Types of angles
• Acute angle
• Obtuse angle
• Right angle
• Adjacent angles
• Complementary angles
• Supplementary angles
• Geometry theorems
• Vertical angle theorem
• Straight angle
• Angles point
• Pentagon angles

Practice measuring angles questions

1. What is the measure of angle LMN to the nearest degree?

The vertex is placed correctly on the protractor and the arm is lined up correctly on the bottom of the protractor.

The other arm goes through the 150^{\circ} and 30^{\circ} . Since the angle is obtuse, the correct measure is 150^{\circ} .

2. Which angle has a measure closest to 85^{\circ} ?

The angle is an acute angle because 85^{\circ} is less than 90^{\circ} .

These angles are larger than 90 degrees and appear to be obtuse.

This angle is acute, however, the measure is less than 85 degrees.

This angle shows a measure of 85 degrees because the point V is on 0 degrees and point T is on 85 degrees.

3. What is the measure of angle EFG to the nearest degree?

The other arm goes through the 125^{\circ} and 55^{\circ} . Since the angle is acute, the correct measure is 55^{\circ} .

4. Which angle has a measure closest to 115^{\circ} ?

The angle is an obtuse angle because 115^{\circ} is greater than 90^{\circ} .

These angles are smaller than 90 degrees and appear to be acute.

This angle is a straight angle, measuring 180 degrees.

This angle shows a measure of 115 degrees because the point F is on 15 degrees and point D is on 130 degrees. 130-15=115 degrees.

5. What is the measure of angle XYZ to the nearest degree?

The angle is a right angle because it appears to be exactly 90^{\circ} .

Using the measures that run from left to right, the arm at point X goes through 60^{\circ} , and the arm at point C goes through 150^{\circ} .

The measure of angle XYZ is 90^{\circ} .

6. Which angle has a measure closest to 90^{\circ} ?

The angle is a right angle because it is equal to 90^{\circ} .

These angles appear to be acute.

This angle appears to be obtuse.

This angle shows a measure of 90 degrees because point N is on 45 degrees and point P is on 135 degrees. 135-45=90 degrees.

Measuring angles FAQs

A straight angle is an angle that measures 180 degrees. A straight angle and a straight line are the same.

A standard protractor can measure up to a 180 degree angle. To measure an angle over 180 degrees, you can measure the angle in smaller parts, and then subtract the total from 360 degrees.

No, the degrees of an angle can involve both fractions and decimals.

Yes, you are able to measure the angles of different polygons. For example, the sum of the interior angles of a triangle is 180 degrees, and the sum of the interior angles of a quadrilateral is 360 degrees.

The next lessons are

• Angles in parallel lines

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Triangle Angle Calculator

Table of contents

Triangle angle calculator is a safe bet if you want to know how to find the angle of a triangle. Whether you have three sides of a triangle given, two sides and an angle or just two angles, this tool is a solution to your geometry problems. Below you'll also find the explanation of fundamental laws concerning triangle angles: triangle angle sum theorem, triangle exterior angle theorem, and angle bisector theorem. Read on to understand how the calculator works, and give it a go - finding missing angles in triangles has never been easier!

How to find the angle of a triangle

There are several ways to find the angles in a triangle, depending on what is given:

• Given three triangle sides

Use the formulas transformed from the law of cosines:

For the second angle we have:

And eventually, for the third angle:

• Given two triangle sides and one angle

If the angle is between the given sides, you can directly use the law of cosines to find the unknown third side, and then use the formulas above to find the missing angles, e.g. given a,b,γ:

• calculate c = a 2 + b 2 − 2 a b × cos ⁡ ( γ ) c = \sqrt{a^2 + b^2 - 2ab \times \cos(\gamma)} c = a 2 + b 2 − 2 ab × cos ( γ ) ​ ;
• substitute c c c in α = a r c c o s ( ( b 2 + c 2 − a 2 ) / ( 2 b c ) ) \alpha = \mathrm{arccos}\left((b^2 + c^2- a^2)/(2bc)\right) α = arccos ( ( b 2 + c 2 − a 2 ) / ( 2 b c ) ) ;
• then find β \beta β from triangle angle sum theorem: β = 180 ° − α − γ \beta = 180\degree- \alpha - \gamma β = 180° − α − γ

If the angle isn't between the given sides, you can use the law of sines. For example, assume that we know a a a , b b b , and α \alpha α :

• As you know, the sum of angles in a triangle is equal to 180 ° 180\degree 180° . From this theorem we can find the missing angle: γ = 180 ° − α − β \gamma = 180\degree- \alpha - \beta γ = 180° − α − β .
• Given two angles

That's the easiest option. Simply use the triangle angle sum theorem to find the missing angle:

• α = 180 ° − β − γ \alpha = 180\degree- \beta - \gamma α = 180° − β − γ ;
• β = 180 ° − α − γ \beta= 180\degree- \alpha - \gamma β = 180° − α − γ ; and
• γ = 180 ° − α − β \gamma = 180\degree- \alpha- \beta γ = 180° − α − β

In all three cases, you can use our triangle angle calculator - you won't be disappointed.

🙋 Meet the law of sines and cosines at our law of cosines calculator and law of sines calculator ! Everything will be clear afterward. 😉

Sum of angles in a triangle - Triangle angle sum theorem

The theorem states that interior angles of a triangle add to 180 ° 180\degree 180° :

How do we know that? Look at the picture: the angles denoted with the same Greek letters are congruent because they are alternate interior angles. Sum of three angles α \alpha α β \beta β , γ \gamma γ is equal to 180 ° 180\degree 180° , as they form a straight line. But hey, these are three interior angles in a triangle! That's why α + β + γ = 180 ° \alpha + \beta+ \gamma = 180\degree α + β + γ = 180° .

Exterior angles of a triangle - Triangle exterior angle theorem

An exterior angle of a triangle is equal to the sum of the opposite interior angles .

• Every triangle has six exterior angles (two at each vertex are equal in measure).
• The exterior angles, taken one at each vertex, always sum up to 360 ° 360\degree 360° .
• An exterior angle is supplementary to its adjacent triangle interior angle.

Angle bisector of a triangle - Angle bisector theorem

Angle bisector theorem states that:

An angle bisector of a triangle angle divides the opposite side into two segments that are proportional to the other two triangle sides.

Or, in other words:

The ratio of the B D ‾ \overline{BD} B D length to the D C ‾ \overline{DC} D C length is equal to the ratio of the length of side A B ‾ \overline{AB} A B to the length of side A C ‾ \overline{AC} A C :

Finding missing angles in triangles - example

OK, so let's practice what we just read. Assume we want to find the missing angles in our triangle. How to do that?

• Find out which formulas you need to use . In our example, we have two sides and one angle given. Choose angle and 2 sides option.
• Type in the given values . For example, we know that a = 9   i n a = 9\ \mathrm{in} a = 9   in , b = 14   i n b = 14\ \mathrm{in} b = 14   in , and α = 30 ° \alpha = 30\degree α = 30° . If you want to calculate it manually, use law of sines:
• From the theorem about sum of angles in a triangle, we calculate that γ = 180 ° − α − β = 180 ° − 30 ° − 51.06 ° = 98.94 ° \gamma = 180\degree- \alpha - \beta = 180\degree- 30\degree - 51.06\degree= 98.94\degree γ = 180° − α − β = 180° − 30° − 51.06° = 98.94° .
• The triangle angle calculator finds the missing angles in triangle . They are equal to the ones we calculated manually: β = 51.06 ° \beta = 51.06\degree β = 51.06° , γ = 98.94 ° \gamma = 98.94\degree γ = 98.94° ; additionally, the tool determined the last side length: c = 17.78   i n c = 17.78\ \mathrm{in} c = 17.78   in .

Reasoning similar to the one we applied in this calculator appears in other triangle calculations, for example the ones we use in the ASA triangle calculator and the SSA triangle calculator !

How do I find angles in a triangle?

To determine the missing angle(s) in a triangle, you can call upon the following math theorems:

• The fact that the sum of angles is a triangle is always 180° ;
• The law of cosines ; and
• The law of sines .

Which set of angles can form a triangle?

Every set of three angles that add up to 180° can form a triangle. This is the only restriction when it comes to building a triangle from a given set of angles.

Why can't a triangle have more than one obtuse angle?

This is because the sum of angles in a triangle is always equal to 180° , while an obtuse angle has more than 90° degrees. If you had two or more obtuse angles, their sum would exceed 180° and so they couldn't form a triangle. For the same reason, a triangle can't have more than one right angle!

How do I find angles of the 3 4 5 triangle?

Let's denote a = 5 , b = 4 , c = 3 .

• Write down the law of cosines 5² = 3² + 4² - 2×3×4×cos(α) . Rearrange it to find α , which is α = arccos(0) = 90° .
• You can repeat the above calculation to get the other two angles.
• Alternatively, as we know we have a right triangle, we have b/a = sin β and c/a = sin γ .
• Either way, we obtain β ≈ 53.13° and γ ≈ 36.87 .
• We quickly verify that the sum of angles we got equals 180° , as expected.

Angle selection

© Omni Calculator

Side length a

Side length b

Side length c

Solving for measures of angles

What is an angle, and how do we measure it?

In this lesson we’ll look at how to find the measures of angles, in degrees, algebraically.

Hi! I'm krista.

I create online courses to help you rock your math class. Read more.

The measure of angles

An angle is a fraction of a circle, the turn of the angle is measured in degrees (or radians).

The name of this angle is ???\angle ABC???. When we talk about the measure of the angle we use an ???m??? in front of the angle sign, ???m\angle ABC=110{}^\circ???.

Angle addition

The parts of an angle add to the entire angle.

Here you can see that ???m\angle ABC=m\angle ABD+m\angle DBC???. This means if you know ???m\angle DBC=55{}^\circ??? and ???m\angle ABC=110{}^\circ??? you can find ???m\angle ABD???.

???m\angle ABC=m\angle ABD+m\angle DBC???

???110{}^\circ =m\angle ABD+55{}^\circ???

???55{}^\circ =m\angle ABD???

How to add and subtract angles to find their measures

Take the course

Want to learn more about geometry i have a step-by-step course for that. :), solving for angle measures.

If ???m\angle AED=80{}^\circ??? and ???m\angle AEB=30{}^\circ???, what is ???m\angle BEC????

Let’s organize what we know. Looking at the diagram we can see that ???\angle AEB??? is congruent to ???\angle CED???. So we know both angles measure the same, ???m\angle AEB=m\angle CED=30{}^\circ???.

We also know the measure of the entire angle ???m\angle AED=80{}^\circ???. Also ???m\angle AED=m\angle AEB+m\angle BEC+m\angle CED???. Let’s rename ???m\angle BEC??? with the variable ???x???. Then we get

???m\angle AED=m\angle AEB+m\angle BEC+m\angle CED???

???80{}^\circ =30{}^\circ +x+30{}^\circ???

???80{}^\circ =60{}^\circ +x???

???x=20{}^\circ???

So ???m\angle BEC=20{}^\circ???.

Here’s another type of problem you might see.

Find the angle measure of ???\angle 2??? in degrees.

???m\angle 1=2x{}^\circ???

???m\angle 2=5x{}^\circ +5{}^\circ???

???m\angle AGC=105{}^\circ -3x{}^\circ???

We can set up an equation, solve for ???x???, then substitute back in to find ???m\angle 2???.

???m\angle 1+m\angle 2=m\angle AGC???

???2x{}^\circ +5x{}^\circ +5{}^\circ =105{}^\circ -3x{}^\circ???

???7x{}^\circ +5{}^\circ =105{}^\circ -3x{}^\circ???

???7x{}^\circ +3x{}^\circ +5{}^\circ =105{}^\circ???

???10x{}^\circ +5{}^\circ =105{}^\circ???

???10x{}^\circ =100{}^\circ???

???x{}^\circ =10{}^\circ???

Substituting into ???m\angle 2=5x{}^\circ +5{}^\circ???, we get ???m\angle 2=5(10){}^\circ +5{}^\circ =55{}^\circ???.

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7.1.2: Properties of Angles

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Learning Objectives

• Identify parallel and perpendicular lines.
• Find measures of angles.
• Identify complementary and supplementary angles.

Introduction

Imagine two separate and distinct lines on a plane. There are two possibilities for these lines: they will either intersect at one point, or they will never intersect. When two lines intersect, four angles are formed. Understanding how these angles relate to each other can help you figure out how to measure them, even if you only have information about the size of one angle.

Parallel and Perpendicular

Parallel lines are two or more lines that never intersect. Likewise, parallel line segments are two line segments that never intersect even if the line segments were turned into lines that continued forever. Examples of parallel line segments are all around you, in the two sides of this page and in the shelves of a bookcase. When you see lines or structures that seem to run in the same direction, never cross one another, and are always the same distance apart, there’s a good chance that they are parallel.

Perpendicular lines are two lines that intersect at a 90 o (right) angle. And perpendicular line segments also intersect at a 90 o (right) angle. You can see examples of perpendicular lines everywhere as well: on graph paper, in the crossing pattern of roads at an intersection, to the colored lines of a plaid shirt. In our daily lives, you may be happy to call two lines perpendicular if they merely seem to be at right angles to one another. When studying geometry, however, you need to make sure that two lines intersect at a 90 o angle before declaring them to be perpendicular.

The image below shows some parallel and perpendicular lines. The geometric symbol for parallel is ||, so you can show that \(\ \overleftrightarrow{A B} \| \overleftrightarrow{C D}\). Parallel lines are also often indicated by the marking >> on each line (or just a single > on each line). Perpendicular lines are indicated by the symbol \(\ \perp\), so you can write \(\ \overleftrightarrow{W X} \perp \overleftrightarrow{Y Z}\).

If two lines are parallel, then any line that is perpendicular to one line will also be perpendicular to the other line. Similarly, if two lines are both perpendicular to the same line, then those two lines are parallel to each other. Let’s take a look at one example and identify some of these types of lines.

Identify a set of parallel lines and a set of perpendicular lines in the image below.

\(\ \overleftrightarrow{W X} \| \overleftrightarrow{Y Z}\)

\(\ \overleftrightarrow{A B} \perp \overleftrightarrow{W X}, \overleftrightarrow{A B} \perp \overleftrightarrow{Y Z}\)

Which statement most accurately represents the image below?

• \(\ \overleftrightarrow{E F} \| \overleftrightarrow{G H}\)
• \(\ \overleftrightarrow{A B} \perp \overleftrightarrow{E G}\)
• \(\ \overleftrightarrow{F H} \| \overleftrightarrow{E G}\)
• \(\ \overleftrightarrow{A B} \| \overleftrightarrow{F H}\)
• Incorrect. This image shows the lines \(\ \overleftrightarrow{E G}\) and \(\ \overleftrightarrow{F H}\), not \(\ \overleftrightarrow{E F}\) and \(\ \overleftrightarrow{G H}\). Both \(\ \overleftrightarrow{E G}\) and \(\ \overleftrightarrow{F H}\) are marked with >> on each line, and those markings mean they are parallel. The correct answer is \(\ \overleftrightarrow{F H} \| \overleftrightarrow{E G}\).
• Incorrect. \(\ \overleftrightarrow{A B}\) does intersect \(\ \overleftrightarrow{E G}\), but the intersection does not form a right angle. This means that they cannot be perpendicular. The correct answer is \(\ \overleftrightarrow{F H} \| \overleftrightarrow{E G}\).
• Correct. Both \(\ \overleftrightarrow{E G}\) and \(\ \overleftrightarrow{F H}\) are marked with >> on each line, and those markings mean they are parallel.
• Incorrect. \(\ \overleftrightarrow{A B}\) and \(\ \overleftrightarrow{F H}\) intersect, so they cannot be parallel. Both \(\ \overleftrightarrow{E G}\) and \(\ \overleftrightarrow{F H}\) are marked with >> on each line, and those markings mean they are parallel. The correct answer is \(\ \overleftrightarrow{F H} \| \overleftrightarrow{E G}\).

Finding Angle Measurements

Understanding how parallel and perpendicular lines relate can help you figure out the measurements of some unknown angles. To start, all you need to remember is that perpendicular lines intersect at a 90 o angle, and that a straight angle measures 180 o .

The measure of an angle such as \(\ \angle A\) is written as \(\ m \angle A\). Look at the example below. How can you find the measurements of the unmarked angles?

Find the measurement of \(\ \angle I J F\).

\(\ m \angle I J F=90^{\circ}\)

In this example, you may have noticed that angles \(\ \angle H J I, \angle I J F, \text { and } \angle H J M\) are all right angles. (If you were asked to find the measurement of \(\ \angle F J M\), you would find that angle to be 90 o , too.) This is what happens when two lines are perpendicular: the four angles created by the intersection are all right angles.

Not all intersections happen at right angles, though. In the example below, notice how you can use the same technique as shown above (using straight angles) to find the measurement of a missing angle.

Find the measurement of \(\ \angle D A C\).

\(\ m \angle D A C=45^{\circ}\)

Find the measurement of \(\ \angle C A D\).

Supplementary and Complementary

In the example above, \(\ m \angle B A C\) and \(\ m \angle D A C\) add up to 180 o . Two angles whose measures add up to 180 o are called supplementary angles . There’s also a term for two angles whose measurements add up to 90 o ; they are called complementary angles .

One way to remember the difference between the two terms is that “corner” and “complementary” each begin with c (a 90 o angle looks like a corner), while straight and “supplementary” each begin with s (a straight angle measures 180 o ).

If you can identify supplementary or complementary angles within a problem, finding missing angle measurements is often simply a matter of adding or subtracting.

Two angles are supplementary. If one of the angles measures 48 o , what is the measurement of the other angle?

The measurement of the other angle is 132 o .

Find the measurement of \(\ \angle A X Z\).

\(\ m \angle A X Z=150^{\circ}\)

Find the measurement of \(\ \angle B A C\).

\(\ m \angle B A C=40^{\circ}\)

\(\ m \angle C A D=80^{\circ}\)

Exercise \(\PageIndex{1}\)

Which pair of angles is complementary?

• \(\ \angle P K O \text { and } \angle M K N\)
• \(\ \angle P K O \text { and } \angle P K M\)
• \(\ \angle L K P \text { and } \angle L K N\)
• \(\ \angle L K M \text { and } \angle M K N\)
• Incorrect. The measures of complementary angles add up to 90 o . It looks like the measures of these angles may add up to 90 o , but there is no way to be sure, so you cannot say that they are complementary. The correct answer is \(\ \angle L K M \text { and } \angle M K N\).
• Incorrect. \(\ \angle P K O \text { and } \angle P K M\) are supplementary angles (not complementary angles) because together they comprise the straight angle \(\ \angle O K M\). The correct answer is \(\ \angle L K M \text { and } \angle M K N\).
• Incorrect. \(\ \angle L K P \text { and } \angle L K N\) are supplementary angles (not complementary angles) because together they comprise the straight angle \(\ \angle P K N\). The correct answer is \(\ \angle L K M \text { and } \angle M K N\).
• Correct. The measurements of two complementary angles will add up to 90 o . \(\ \angle L K P\) is a right angle, so \(\ \angle L K N\) must be a right angle as well. \(\ \angle L K M+\angle M K N=\angle L K N\), so \(\ \angle L K M \text { and } \angle M K N\) are complementary.

Parallel lines do not intersect, while perpendicular lines cross at a 90 o . angle. Two angles whose measurements add up to 180 o are said to be supplementary, and two angles whose measurements add up to 90 o are said to be complementary. For most pairs of intersecting lines, all you need is the measurement of one angle to find the measurements of all other angles formed by the intersection.

Triangle Calculator

Enter the values of any two angles and any one side of a triangle below which you want to solve for remaining angle and sides.

Triangle calculator finds the values of remaining sides and angles by using Sine Law.

Sine law states that

a sin A = b sin B = c sin C

Cosine law states that-

a 2 = b 2 + c 2 - 2 b c . cos ( A ) b 2 = a 2 + c 2 - 2 a c . cos ( B ) c 2 = a 2 + b 2 - 2 a b . cos ( C )

Click the blue arrow to submit. Choose "Solve the Triangle" from the topic selector and click to see the result in our Trigonometry Calculator!

Solve the Triangle

Triangles Calculator

Calculate area, perimeter, sides and angles for triangles step-by-step.

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