The measure of an angle which is four times its supplement is(a) 36°

1.	The measure of an angle which is four times its supplement is(a) 36° (b) 144° (c) 16° (d) 64°
Answer» Let the measure of the angle be x°. According to the question, x=4(180°-x) =>x=720°-4x =>5x=720° =>x=720°/5=144°(B) Let the required angle be θ ∴ supplementary angle =180^∘− θ ∴ θ = 4 × (180^∘− θ) ⇒ 5θ = 720^∘ ⇒ θ = 720^∘/5 ∴ θ = 144^∘

The measure of an angle which is four times its supplement is(a) 36° (b) 144° (c) 16° (d) 64°

Answer» Let the measure of the angle be x°.

According to the question, x=4(180°-x)

=>x=720°-4x

=>5x=720°

=>x=720°/5=144°(B)

Let the required angle be θ

∴ supplementary angle =180^∘− θ

∴ θ = 4 × (180^∘− θ)

⇒ 5θ = 720^∘

⇒ θ = 720^∘/5

∴ θ = 144^∘