Question

In the given figure lines $\overleftrightarrow{XY}$ and $\overleftrightarrow{MN}$ intersect at O. If $\angle POY={90}^o$ and a: b = 2 : 3, find $\angle$ c.

Answer 1

$a:b=2:3$

Let $a=2x$ and $b=3x$

$\angle POX={90}^{\circ }$

$\angle POM+\angle MOX={90}^{\circ }2x+3x={90}^{\circ }\Rightarrow x=\frac{{90}^{\circ }}{5}={18}^{\circ }\Rightarrow \angle POM=2x=2\times {18}^{\circ }={36}^{\circ }\Rightarrow \angle MOX=3x=3\times {18}^{\circ }={54}^{\circ }$

$\angle MOX+\angle XON={180}^{\circ }$ (Angles made on line $MN$)

${54}^{\circ }+\angle XON={180}^{\circ }\angle XON={180}^{\circ }-{54}^{\circ }={126}^{\circ }$

$c={126}^{\circ }$