Question

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

• A. ${126}^{\circ }$
• B. ${36}^{\circ }$
• C. ${54}^{\circ }$
• D. ${90}^{\circ }$

Answer 1

The correct option is A

${126}^{\circ }$

We have, a : b = 2:3

So, let a= 2x and b=3x

Clearly,ray OP stands on line XY.

$\angle XOP+\angle POY={180}^{\circ }$ [Linear pair of angles]

$a+b+{90}^{\circ }={180}^{\circ }$

$a+b={180}^{\circ }-{90}^{\circ }$

$a+b={90}^{\circ }$

$2x+3x={90}^{\circ }$

$5x={90}^{\circ }$

$x={18}^{\circ }$

$a=2x={36}^{\circ }$

$b=3x={54}^{\circ }$

$b+c={180}^{\circ }$

$c={180}^{\circ }-{54}^{\circ }={126}^{\circ }$