Question

The sum of an angle and one third of its supplementary angle is ${90}^{\circ }$. The measure of the angle is
(a) ${135}^{\circ }$
(b) ${120}^{\circ }$
(c) ${60}^{\circ }$
(d) ${45}^{\circ }$

Answer 1

Let the required angle be $x^{\circ }$.
Now, supplementary of the required angle $={180}^{\circ }-x$
Then, the given condition $x^{\circ }+\frac{1}{3}({180}^{\circ }-x^{\circ })={90}^{\circ }$
$\Rightarrow \frac{3x+180-x}{3}=90$
$\Rightarrow \frac{2x+180}{3}=90$
$\Rightarrow 2x+180=270$
$\Rightarrow 2x=270-180$
$\Rightarrow x=\frac{90}{2}$
$\therefore x={45}^{\circ }$
Hence, the correct answer is option (d).