Question

Given ∠A and ∠B are supplementary angles, prove that
∠B < 180°. Furthermore, if ratio of A : B is 1 : 2, find the value of ∠B.
[ 3 Marks]

Answer 1

Given A and B are supplementary angles,
Then A + B = 180°
To prove: B < 180°

Let B is ≥ 180°.
Then A + B ≥ 180° + A
⇒ A + B > 180° (because A and B are angles and cannot be negative)
[1 Mark]

This is absurd because A + B = 180°.
Hence, our assumption is wrong, B < 180°.
[1 Mark]

As sum of supplementary angles is 180°, if the ratio of ∠A : ∠B = 1 : 2,
x + 2x = 180°
3x = 180°.
x = 60°
[1 Mark]