Angle pairs
Two angles can work together to make a right angle or a straight angle.
| Pair | Add up to | Forms |
|---|---|---|
| Complementary angles | 90° | a right angle (corner) |
| Supplementary angles | 180° | a straight angle (straight line) |
Memory trick: C comes before S in the alphabet, and 90 comes before 180. Or: "Complementary makes a Corner; Supplementary makes a Straight line."
Finding the complement
The complement of an angle is 90° minus the angle.
- Complement of 35° = 90° − 35° = 55°
- Complement of 72° = 18°
Only acute angles have complements (an obtuse angle is already more than 90°).
Finding the supplement
The supplement is 180° minus the angle.
- Supplement of 35° = 180° − 35° = 145°
- Supplement of 120° = 60°
Adjacent angles
Adjacent angles share a vertex and a side, sitting side by side. Complementary or supplementary angles are often adjacent, but they don’t have to be: any two angles that add to 90° are complementary, wherever they are.
Angles on a straight line
Angles that sit together on a straight line always add to 180°.
Example: A straight line is split into angles of x and 3x.
- x + 3x = 180
- 4x = 180
- x = 45°, and 3x = 135°
Angles in a right angle
Example: A right angle is split into angles 2y and y + 30.
- 2y + y + 30 = 90
- 3y = 60
- y = 20° → angles are 40° and 50°
Angles around a point
All angles around a point add to 360°.
Worked examples
Example 1: Find the complement of 28°.
90 − 28 = 62°.
Example 2: Two supplementary angles are equal. How big is each?
180 ÷ 2 = 90°.
Example 3: One angle is 4 times its complement. Find both.
x + 4x = 90 → x = 18 → 18° and 72°.
Common mistakes
- Mixing up 90° and 180°.
- Trying to find the complement of an obtuse angle.
- Forgetting to answer both angles in algebra problems.
Try it yourself
- Complement of 47°
- Supplement of 47°
- Two angles on a straight line are 3x and 2x. Find x.
- An angle and its supplement differ by 40°. Find them.
Answers: 1) 43° 2) 133° 3) 36° 4) 110° and 70°
Quick recap
- Complementary angles add to 90°; supplementary angles add to 180°.
- Complement = 90° − angle; supplement = 180° − angle.
- Angles on a straight line add to 180°; around a point, 360°.