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.

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.

Summary of Key Facts

Concept	Rule
Angles in a straight line	Add up to 180°
Angles at a point	Add up to 360°

Exercise

(a)

Find the value of x.

Check Answer
Show Working
60° + 87° + x = 180°
147° + x = 180°
x = 180° − 147°
x = 33°

(b)

Find the value of x.

Check Answer
Show Working
x + 3x = 180°
4x = 180°
x = 45°

(c)

Find the value of x.

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

(d)

Find the value of x.

Check Answer
Show Working
x + 3x + 5x = 360°
9x = 360°
x = 40°