An angle is one-fifth of its supplement. The measure of the angle is

Question:

An angle is one-fifth of its supplement. The measure of the angle is
(a) 15°
(b) 30°
(c) 75°
(d) 150°

Solution:

(b) 30°

Let the measure of the required angle be $x^{\circ}$

Then, the measure of its supplement will be $(180-x)^{\circ}$

$\therefore x=\frac{1}{5}\left(180^{\circ}-x\right)$

$\Rightarrow 5 x=180^{\circ}-x$

$\Rightarrow 6 x=180^{\circ}$

$\Rightarrow x=30^{\circ}$

 

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