Angle Relationships • Topic 1 of 3

Complementary & Supplementary Angles

What are Complementary Angles?

Two angles are complementary if their measures add up to 90°.

Each angle is called the complement of the other
They don't have to be adjacent (next to each other)

Example: 30° + 60° = 90° → Complementary

What are Supplementary Angles?

Two angles are supplementary if their measures add up to 180°.

Each angle is called the supplement of the other
They don't have to be adjacent

Example: 110° + 70° = 180° → Supplementary

COMPLEMENTARY ANGLES (sum = 90°):

    Adjacent Complementary:     Non-adjacent Complementary:
    
         /|
        / | 30°                    30°
       /  |                          60°
      /   | 60°
     /    |
    └─────┘
    
    30° + 60° = 90°             30° + 60° = 90°


SUPPLEMENTARY ANGLES (sum = 180°):

    Adjacent Supplementary (Linear Pair):   Non-adjacent:
    
        ┌─────────┐
        │         │
        │  120°   │       120°        60°
        │         │
        └─────────┘
    
    120° + 60° = 180°           120° + 60° = 180°


FINDING COMPLEMENTARY ANGLE:

    If one angle is 35°, complement = 90° - 35° = 55°
    If one angle is 72°, complement = 90° - 72° = 18°


FINDING SUPPLEMENTARY ANGLE:

    If one angle is 115°, supplement = 180° - 115° = 65°
    If one angle is 45°, supplement = 180° - 45° = 135°

Solved Examples

Worked Example

Are 35° and 55° complementary?

Solution

35° + 55° = 90°
Yes, they are complementary
Answer: Yes

Worked Example

Find the supplement of a 125° angle.

Solution

Supplement = 180° - 125° = 55°
Answer: 55°

Worked Example

Two angles are complementary. One is 3 times the other. Find both angles.

Solution

Let smaller = x, larger = 3x
x + 3x = 90°
4x = 90°
x = 22.5°, 3x = 67.5°
Answer: 22.5° and 67.5°

Worked Example

An angle is 30° more than its supplement. Find the angle.

Solution

Let angle = x, supplement = 180° - x
x = (180° - x) + 30°
x = 210° - x
2x = 210°
x = 105°
Answer: 105°

Key Points

Complementary: sum = 90°
Supplementary: sum = 180°
Complement = 90° - angle
Supplement = 180° - angle
Angles don't have to be adjacent

Quick Check — 4 MCQs

Tap an option to check your answer0 / 4

Q1.Two angles are complementary if they sum to:

Explanation: $90^\circ$.

Q2.Two angles are supplementary if they sum to:

Explanation: $180^\circ$.

Q3.The complement of $40^\circ$ is:

Explanation: $90-40$.

Q4.The supplement of $110^\circ$ is:

Explanation: $180-110$.

Practice more MCQs → 📝 Assignment · 35 marks