Question

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

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

Answer 1

The correct option is D

${63}^{\circ }$

Given, $\angle POY={90}^{\circ }$

A:B = 2:3

Let A be 2x and B be 3x.

$A+B+\angle POY={180}^{\circ }$ (∵ 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.
Therefore,

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

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

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

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