Lines and angles
An angle is the amount of turn between two rays that meet at a common point called the vertex. We measure angles in degrees (°) using a protractor. A full turn is 360°.
Angles are grouped by size:
- Acute angle: between 0° and 90°.
- Right angle: exactly 90° (a square corner).
- Obtuse angle: between 90° and 180°.
- Straight angle: exactly 180° (a straight line).
- Reflex angle: between 180° and 360°.
Angle rules you must know
Key idea / 要点
Angles on a straight line add up to 180°. Angles at a point (all the way round) add up to 360°.
Two special pairs:
- Complementary angles add up to 90°.
- Supplementary angles add up to 180°.
Finding an unknown angle
Write down the rule, subtract the known angles, and check your answer is sensible.
Worked example / 例题
Three angles ∠a, 65° and 90° sit on a straight line. Find ∠a.
Angles on a straight line add up to 180°, so:
∠a = 180° − 65° − 90° = 25°.
Check: 25° + 65° + 90° = 180°. Correct, and 25° is acute, which looks right.
Remember / 记住
- Straight line → 180°; around a point → 360°.
- Complementary → 90°; supplementary → 180°.
- Always name the rule before you calculate.