Question

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

Answer 1

$$\begin{lgathered}\sf{\huge{Heya\:mate.\: Solution\\below.}}\end{lgathered}$$

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★ $$Answer - ↓↓↓$$ ★

♠ $$\sf{\underline{Supplementary \: angles\: -}}$$

Two angles whose sum is 180° are called Supplementary angles.

♠ So, let the angle be 'x'.

Then, it's supplement would be = 180° - x

♠ Now, according to the question, the angle is four times it's supplement.

$$\sf{=> 4(x) = 180 - x}$$

$$\sf{=> 4x + x = 180}$$

$$\sf{=> 5x = 180}$$

$$\sf{=> x = \frac{180}{5}}$$

$$\sf{=> x = 36}$$

♠ So, x = 36°

♠ Now, the angles is 4 times it's supplement. So, the angles is,

$$\sf{= 4 \times x}$$

$$\sf{= 4 \times 36}$$

$$\sf{= 144°}$$

♥ •°• The angle is 144°. ♥

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Thank you... (^_-)