Question

Given ∠A and ∠B are complementary angles, prove that
∠B < 90°. 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 = 90°

To prove: B < 90°

Let B is ≥ 90°

Then A + B ≥ 90° + A

⇒ A + B > 90° (because A and B are angles and cannot be negative)
[1 Mark]

This is absurd because A + B = 90°.

Hence, our assumption is wrong and B < 90°
[1 Mark]

As sum of supplementary angles is 90°, and the ratio of ∠A : ∠B = 1 : 2,

$\Rightarrow$ x + 2x = 90°

3x = 90°

x =$\frac{{90}^{\circ }}{3}$
= 30°

$\therefore$ ∠B = 2x = 60°.
[1 Mark]