Angle Relationships

A free Geometry lesson from the “Geometry Foundations” unit, with a worked example and practice problems including step-by-step solutions.

Complementary angles add to 90 degrees, supplementary angles add to 180 degrees, and vertical angles formed by intersecting lines are congruent.

What you'll learn

Why it matters: Architects and carpenters use angle relationships when fitting beams, trim, and corners that must meet cleanly.

Problem. Two supplementary angles measure x and 115 degrees. Find x.

Answer: 65 degrees

1. An angle is complementary to 38 degrees. What is its measure?

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Warm-up: First identify exactly what the question is asking: An angle is complementary to 38 degrees. What is its measure?
Use the relevant geometric relationship first, then set up an equation from the angle measures or side relationships.
Complementary angles add to 90.
90 - 38 = 52.
Check the result by substituting or estimating: the response should match 52 and make sense in the original problem.

Answer: 52

2. Two angles add to 180 degrees. What are they called?

Choices: Complementary · Supplementary · Vertical · Adjacent

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Warm-up: First identify exactly what the question is asking: Two angles add to 180 degrees. What are they called?
Use the relevant geometric relationship first, then set up an equation from the angle measures or side relationships.
Supplementary angles add to 180 degrees.
Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.

Answer: Supplementary

3. An angle is supplementary to 104 degrees. What is its measure?

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Core Practice: First identify exactly what the question is asking: An angle is supplementary to 104 degrees. What is its measure?
Use the relevant geometric relationship first, then set up an equation from the angle measures or side relationships.
180 - 104 = 76.
Check the result by substituting or estimating: the response should match 76 and make sense in the original problem.

Answer: 76

4. Vertical angles measure 4x and 96 degrees. Find x.

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Core Practice: First identify exactly what the question is asking: Vertical angles measure 4x and 96 degrees. Find x.
Use the relevant geometric relationship first, then set up an equation from the angle measures or side relationships.
Vertical angles are equal.
4x = 96.
Check the result by substituting or estimating: the response should match 24 and make sense in the original problem.

Answer: 24

5. Angles x and 2x form a straight line. Find x.

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Challenge: First identify exactly what the question is asking: Angles x and 2x form a straight line. Find x.
Use the relevant geometric relationship first, then set up an equation from the angle measures or side relationships.
x + 2x = 180.
3x = 180.
Check the result by substituting or estimating: the response should match 60 and make sense in the original problem.

Answer: 60

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