Chapter 4 - Geometry: Angles

4.1.1 ANGLES IN A STRAIGHT LINE

Key Rule:

Angles in a straight line add up to 180°.

This means when angles lie on a straight line, their total sum must equal 180 degrees.

Example 4.1 Diagram
Example 4.2 Diagram

4.1.2 ANGLES AT A POINT

Key Rule:

Angles around a point describe the sum of angles that form a full turn.

Angles at a point add up to 360°.

Example 4.3

Calculate the value of angle a.

Example 4.3 Diagram
Example 4.4 Diagram

Summary of Key Facts

ConceptRule
Angles in a straight lineAdd up to 180°
Angles at a pointAdd up to 360°
Exercise

Exercise

Angles Exercise

(a)

Find the value of x.

60° + 87° + x = 180° 147° + x = 180° x = 180° − 147° x = 33°

(b)

Find the value of x.

x + 3x = 180° 4x = 180° x = 45°

(c)

Find the value of x.

75° + 45° + 83° + x = 360° 203° + x = 360° x = 157°

(d)

Find the value of x.

x + 3x + 5x = 360° 9x = 360° x = 40°