Question

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

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

Given in fig. $\angle$POY = ${90}^{\circ }$

$\angle$A: $\angle$B = 2:3

Let $\angle$A = 2x and $\angle$B = 3x

$\angle$A + $\angle$B + $\angle$POY = ${180}^{\circ }$ (∵ XOY is a line)

2x + 3x + ${90}^{\circ }$ = ${180}^{\circ }$

5x = ${90}^{\circ }$

x = $\frac{90}{5}$ = ${18}^{\circ }$

∴ $\angle$A = ${36}^{\circ }$ , $\angle$B = ${54}^{\circ }$

MON is a line.

$\Rightarrow$ $\angle$B + $\angle$ C = ${180}^{\circ }$

$\Rightarrow$ ${54}^{\circ }$ + $\angle$C = ${180}^{\circ }$

$\Rightarrow$ $\angle$C = ${180}^{\circ }$ – ${54}^{\circ }$ = ${126}^{\circ }$

$\Rightarrow$ $\frac{C}{2}$=${63}^{\circ }$