Question

Q.25 In Fig. lines XY and MN
intersect at O. If angle POY =
90° and a: b = 2:3, find c.

Option:
1)110°
2)116°
3)126°
4)136°​

Answer 1

a:b = 2:3 (given)

angle POY = 90° (given)

let a = 2x

and b= 3x

therefore, a+b+POY=180° (linear pair)

2x + 3x + 90° =180°

5x = 180° - 90°

5x = 90°

x= 90°/5

x= 18°

hence, a = 2x= 2(18°) = 36°

and b = 3x = 3(18°) = 54°

angle b = angle YON (vertical opposite angles)

therefore, angle YON = 54°

Now, angle YON + angle C = 180° (linear pair)

therefore, 54° + C = 180°

C = 180°- 54°

C = 126°

ANSWER IS OPTION 3). 126°