Question

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

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

Given, ∠POY = ${90}^{\circ }$

A:B = 2:3

Let A = 2x and B = 3x.

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

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

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

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

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

Also, MON is a line, so that,

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

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

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

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