Question

If the supplement of an angle is three times its complement, then angle is:

• A. $35°$
• B. $40°$
• C. $45°$
• D. $50°$

Answer 1

The correct option is C

$45°$

Find the required angle.

As we know that, The Complementary angles are two angles whose sum is $90°$

The Supplementary angles are two angles whose sum is $180$ (a straight angle).

Assume that the $\angle x$ be the required angle.

So,

$\Rightarrow$ $180-x=3\left(90-x\right)$

$\Rightarrow$ $180-x=270-3x$

Subtract $180$ from both sides.

$\Rightarrow$ $180-x-180=270-3x-180$

$\Rightarrow$ $-x=-3x+90$

Add $3x$ to both sides by $2$.

$\Rightarrow$ $-x+3x=-3x+90+3x$

$\Rightarrow$ $2x=90$

Divide both sides by $2$.

$\Rightarrow$ $\frac{2x}{2}=\frac{90}{2}$

$\Rightarrow$ $x=45$

Hence, the Option $C$ is correct answer.