Question

If amongst two supplementary angles, the measure of smaller angle is four times its complement, then their difference is:

• A. ${30}^0$
• B. ${36}^0$
• C. ${43}^0$
• D. ${45}^0$

Answer 1

The correct option is B ${36}^0$

Let $x,y$ be any two supplementary angles and $x$ be the smaller angle

$\therefore$ $x+y={180}^o$

Also, $x=4({360}^o-x)$

$⟹$ $x=4\times {360}^o-4x$

$⟹$ $5x=4\times {360}^o$

$⟹$ $x=4\times {72}^o={288}^o$

$x+y={180}^o$ $⟹$ $y=-{108}^o={252}^o$

$\therefore$ $x-y=288-252={36}^o$.

Hence, option B is correct.