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
easySolution
- 1 Supplementary angles add up to 180°.
- 2 Let the unknown angle be x: 115 + x = 180.
- 3 Solve: x = 180 - 115 = 65°.
Answer
Example 2
mediumPractice Problems
Try these problems on your own first, then open the solution to compare your method.
Example 1
easyExample 2
mediumBackground Knowledge
These ideas may be useful before you work through the harder examples.