Question

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

Answer 1

Solution:-

$\angle POY=90°$

$\angle POY+\angle POX=\angle XOY=180°$

$\angle POX=180°-90°=90°$

$\because a:b=2:3$

Therefore,

$a=2x$

$b=3x$

$\angle POX=a+b=90°$

$\Rightarrow 2x+3x=90°$

$\Rightarrow 5x=90°$

$\Rightarrow x=\frac{90}{5}=18°$

$\therefore a=2\times 18=36°$

$b=3\times 18°=54°$

$\angle MON=b+c=180°$

$54°+c=180°$

$\Rightarrow c=180°-54°=126°$