Question

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

• A. ${56}^o$
• B. ${126}^o$
• C. ${145}^0$
• D. ${137}^o$

Answer 1

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

Since XOY is a straight line.

Therefore,

$b+a+\angle POY={180}^o$

But, $\angle POY={90}^o$

Thus, $b+a={90}^o$ .......(1)

Also, $a:b=2:3$

$⟹b=\frac{3a}{2}$ .....(2)

Now from 1 and 2, we get,

$\frac{3a}{2}+a={90}^o$

$\frac{5a}{2}={90}^o$

$a=\frac{90}{5}\times 2={36}^o$

$b={54}^o$

Since XY and MN intersect at O.

Therefore,

$c=a+\angle POY$

$c={36}^o+{90}^o={126}^o$