Angle Relationships Examples in Math

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Angle Relationships.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.

Concept Recap

Fundamental relationships between pairs of angles: supplementary angles sum to 180°, complementary angles sum to 90°, vertical angles are equal, and adjacent angles share a common ray.

Think of opening a book flat on a table—the two pages form supplementary angles (they add to a straight line, 180°). Now think of the corner of a room where two walls meet the floor—those two angles are complementary (they add to a right angle, 90°). When two lines cross like an X, the opposite angles are always equal—those are vertical angles.

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How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Angle relationships let you find unknown angles from known ones—they're the 'equations' of geometry.

Common stuck point: Supplementary = 180° (think 'S' for straight line). Complementary = 90° (think 'C' for corner).

Worked Examples

Example 1

easy
Two angles are supplementary. One angle measures 73°. Find the other angle.

Solution

  1. 1
    Step 1: Supplementary angles sum to 180°.
  2. 2
    Step 2: Let the other angle be x. Then 73° + x = 180°.
  3. 3
    Step 3: x = 180° - 73° = 107°.

Answer

The other angle is 107°.
Supplementary angles are two angles whose measures add to 180°. They don't need to be adjacent — any two angles summing to 180° are supplementary. A straight line is formed when supplementary angles are adjacent, which is one common way they appear in geometry problems.

Example 2

medium
Two lines intersect forming four angles. One angle is 124°. Find all four angles.

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy
Angle A and angle B are complementary. If \angle A = 4x + 3° and \angle B = 2x + 9°, find both angles.

Example 2

hard
Three angles share a common vertex and together form a straight line. The angles are in the ratio 1:2:3. Find each angle.
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Background Knowledge

These ideas may be useful before you work through the harder examples.

angles