Geometry · StudentHub Lesson
Angles and Degrees
Classify angles by size and use angle relationships to find unknown measures.
What you will learn
- Define an angle and how it is measured in degrees
- Classify angles as acute, right, obtuse or straight
- Understand complementary and supplementary angles
- Recognise vertical and adjacent angles
- Solve for unknown angles using angle relationships
Watch the lesson
Math Antics - Angles & Degrees · mathantics
Watch on YouTubeTopic notes
Main Idea
An angle is formed by two rays sharing a common endpoint and is measured in degrees based on how much rotation separates the rays.
Key Concepts
- Angles are classified by measure: acute, right, obtuse, straight, reflex
- Complementary angles sum to 90°, supplementary angles sum to 180°
- Vertical angles (formed by intersecting lines) are always equal
Definitions
- Acute angle: less than 90°
- Right angle: exactly 90°
- Obtuse angle: between 90° and 180°
- Straight angle: exactly 180°
Formulas
- Complementary: A + B = 90°
- Supplementary: A + B = 180°
Examples
- If one angle is 35°, its complement is 90-35=55°
- If one angle is 110°, its supplement is 180-110=70°
Common Mistakes
- Confusing complementary (90°) with supplementary (180°)
- Misreading a protractor scale
- Assuming all adjacent angles are equal (only vertical angles are)
Key concepts
Important terms
- Acute angle
- An angle less than 90 degrees.
- Obtuse angle
- An angle between 90 and 180 degrees.
- Complementary angles
- Two angles that add up to 90 degrees.
Worked examples
Problem
Find the complement of a 40° angle
- 1. Complementary angles sum to 90°
- 2. 90-40=50
Answer: 50°
Problem
Find the supplement of a 65° angle
- 1. Supplementary angles sum to 180°
- 2. 180-65=115
Answer: 115°
Quick revision
- Acute: less than 90°
- Right angle: exactly 90°
- Obtuse: between 90° and 180°
- Complementary angles sum to 90°
- Supplementary angles sum to 180°
- Vertical angles are always equal
Check your understanding
Question 1 · Multiple choice
What type of angle measures exactly 90°?
Question 2 · Multiple choice
Two angles are supplementary. One is 120°. What is the other?
Question 3 · Short answer
Find the complement of a 25° angle.
Question 4 · Short answer
Classify a 150° angle.
Question 5 · True or false
Vertical angles formed by two intersecting lines are always equal.
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