Question

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

Answer 1

Given, $\angle POY={90}^{\circ }$ and $a:b=2:3$
According to the question,
$\angle POY+a+b={180}^{\circ }$

$\Rightarrow {90}^{\circ }+a+b={180}^{\circ }$
$\Rightarrow a+b={90}^{\circ }$
Let $a$ be $2x$, then will be $3x$
$\Rightarrow 2x+3x={90}^{\circ }$
$\Rightarrow 5x={90}^{\circ }$
$\Rightarrow x={18}^{\circ }$
$\therefore a=2\times 18={36}^{\circ }$
$b=3\times 18={54}^{\circ }$
$b+c={180}^{\circ }$ $\mid$ Linear Pair
$\Rightarrow {54}^{\circ }+c={180}^{\circ }$
$\Rightarrow c={126}^{\circ }$