Question

An angle is equal to one-third of its supplement. Find its measure in degrees.

• A. 55${}^{\circ }$
• B. 45${}^{\circ }$
• C. 35${}^{\circ }$
• D. 25${}^{\circ }$

Answer 1

The correct option is B 45${}^{\circ }$

Let the measure of the required angle be $x$.

Then, supplement of $x$ = ${180}^{\circ }-x$

It is given that

$\text{Angle}=\frac{1}{3}\text{(Supplement of x)}$

$\Rightarrow x=\frac{1}{3}({180}^{\circ }-x)$

$\Rightarrow 3x={180}^{\circ }-x$

$\Rightarrow 4x={180}^{\circ }$

$\Rightarrow x={45}^{\circ }$

Thus, the measure of the given angle is 45${}^{\circ }$.