Question

In figure, lines XY and MN intersect at O. If $\angle POY={90}^{\circ }$ and a : b = 2 : 3, find a, b and c. [4 MARKS]

Answer 1

Concept: 1 Mark
Application: 1.5 Marks
Answer: 0.5 Mark each

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]

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

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

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

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

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

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

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

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

$b+c={180}^{\circ }$ [Linear pair of angles]

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