How to Find Missing Angles

Missing angle problems become easier when you know which angle rule applies.

Quick idea

Most missing angle problems use angle sums: straight lines make 180 degrees, triangles make 180 degrees, and circles around a point make 360 degrees.

Steps

1. Identify the shape or angle relationship.
2. Write an equation using the correct angle sum.
3. Solve the equation.
4. Check whether the answer is reasonable for the diagram.

Worked example

Find x if x and 65 degrees form a straight line.

Full solution

Step-by-step walkthrough

Step 1

A straight line is 180 degrees.

Step 2

Subtract 65 degrees from 180 degrees.

Step 3

The missing angle is 115 degrees.

Common mistake

Do not trust drawings that are not marked to scale. Use the angle relationships, not how the picture looks.

Practice problems

1. A triangle has angles 50 and 60. Find the third.
2. Two supplementary angles include 38 degrees. Find the other.
3. Angles around a point include 90, 120, and x. Find x.

Answers

1. 70 degrees
2. 142 degrees
3. 150 degrees

Ask Pennpaper to explain it live

If the steps make sense but you still feel stuck, start a Pennpaper lesson and ask the tutor to draw the problem on the whiteboard. Seeing the symbols move step by step is often what makes the concept click.

Related guides

• Congruent Triangles: SSS, SAS, ASA, AAS
• Similar Triangles Explained
• Pythagorean Theorem Explained