Question

In the figure below, lines XY and MN intersect at point O. If $\angle$POY = ${90}^{\circ }$ and A:B = 2:3, 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 = 2x and B = 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, so that, B + C = ${180}^{\circ }$ ${54}^{\circ }$ + C = ${180}^{\circ }$ C = ${180}^{\circ }$ – ${54}^{\circ }$ = ${126}^{\circ }$ $\frac{C}{2}$ = ${63}^{\circ }$