Question

In the figure below, lines XY and MN intersect at point O. If $\angle POY$ = ${90}^{\circ }$ and $\angle A:\angle B=2:3$, $\text{find}\frac{\left(\angle C\right)}{2}$.

• A. ${55}^{\circ }$
• B. ${68}^{\circ }$
• C. ${77.5}^{\circ }$
• D. ${63}^{\circ }$

Answer 1

The correct option is D ${63}^{\circ }$

Given, $\angle POY$ = ${90}^{\circ }$ and
$\angle A:\angle B=2:3$ .
Let, $\angle A$ = 2x and $\angle B$ = 3x.
Hence, $\angle A+\angle B+\angle POY={180}^{\circ }$
(∵ XOY is a straight line)
$\Rightarrow$ 2x + 3x + ${90}^{\circ }$ = ${180}^{\circ }$
$\Rightarrow x=\frac{90}{5}={18}^{\circ }$
$\therefore A={36}^{\circ }$, $B={54}^{\circ }$
Also, MON is a straight line, so,
$\angle B+\angle C={180}^{\circ }$
$\Rightarrow$ ${54}^{\circ }+\angle C={180}^{\circ }$
$\Rightarrow$ $\angle C={180}^{\circ }–{54}^{\circ }={126}^{\circ }$
$\Rightarrow \frac{\left(\angle C\right)}{2}={63}^{\circ }$