Question

In the figure given, lines XY and MN intersect at O. If $\angle$POY$={90}^o$ and $a:b=2:3$, then $\angle$XON is equal to ____________.

• A. ${126}^o$
• B. ${30}^o$
• C. ${90}^o$
• D. ${180}^o$

Answer 1

The correct option is A ${126}^o$

If $\angle POY=90$, then $\angle POX={90}^{\circ }$

$\angle POX=a+b$

It is given that, $\frac{a}{b}=\frac{2}{3}$

$\Rightarrow a=\frac{2}{3}b$

$\therefore \frac{2}{3}b+b=90\Rightarrow \frac{5}{3}b=90\Rightarrow b=18\times 3={54}^{\circ }$

For the value of $\angle XON$, as we can see

$\angle XON+b={180}^{\circ }\Rightarrow \angle XON={126}^{\circ }$