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.

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Solution

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)

This is absurd because A + B = 180°.

Hence, our assumption is wrong.

B < 180°

As sum of supplementary angles is 180°,

If the ratio of ∠A : ∠B = 1 : 2,

x + 2x = 180°

3x = 180°.

x = $\frac{180}{30}$ = 60°

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