Angles Examples in Math

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

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

Concept Recap

The amount of rotation between two rays that share a common endpoint, measured in degrees or radians.

Opening a door wider makes a bigger angle; a corner of a book is 90°.

Read the full concept explanation →

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: Angles measure rotation, not length. A full rotation is 360°.

Common stuck point: Acute (< 90°), Right (= 90°), Obtuse (> 90° but < 180°).

Sense of Study hint: Try opening a book to different widths and classifying each opening as acute, right, or obtuse before estimating degrees.

Worked Examples

Example 1

easy
Two angles are supplementary. One measures 115°. Find the other.

Solution

  1. 1
    Supplementary angles add up to 180°.
  2. 2
    Let the unknown angle be x: 115 + x = 180.
  3. 3
    Solve: x = 180 - 115 = 65°.

Answer

x = 65°
Supplementary angles form a straight line (180°). This relationship appears frequently when working with parallel lines and transversals.

Example 2

medium
Two parallel lines are cut by a transversal. One of the alternate interior angles measures 72°. Find all eight angles formed.

Practice Problems

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

Example 1

easy
Two angles are complementary. One measures 37°. Find the other.

Example 2

medium
An exterior angle of a triangle measures 124°. One remote interior angle measures 47°. Find the other remote interior angle.

Background Knowledge

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

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