In Fig. 6.14, lines XY and MN intersect at O. If ∠POY = 90° and a : b = 2 : 3, find c.
Solution:
Given: ∠POY= 90° and a : b = 2 : 3.
If two lines intersect with each other, then the vertically opposite angles formed are equal.
Line OP is perpendicular to line XY. Hence ∠POY = ∠POX = 90°
∠POX = ∠POM + ∠MOX
90° = a + b ….(1)
Since a and b are in the ratio 2 : 3 that is,
a = 2x and b = 3x ….(2)
Substituting (2) in (1),
a + b = 90°
2x + 3x = 90°
5x = 90°
x = 90°/5 = 18°
a = 2x = 2 × 18°
a = 36°
b = 3x = 3 × 18°
b = 54°
Also , ∠MOY= ∠MOP + ∠POY
= a + 90°
= 36° + 90° = 126°
Lines MN and XY intersect at point O and the vertically opposite angles formed are equal.
∠XON = ∠MOY
c = 126°
☛ Check: NCERT Solutions for Class 9 Maths Chapter 6
Video Solution:
In Fig. 6.14, lines XY and MN intersect at O. If ∠POY = 90° and a : b = 2 : 3, find c.
NCERT Solutions Class 9 Maths Chapter 6 Exercise 6.1 Question 2
Summary:
If the given figure lines XY and MN intersect at O, given that ∠POY = 90°, and a : b = 2 : 3, thus, ∠XON = c = 126°.
☛ Related Questions:
- In Fig. 6.13, lines AB and CD intersect at O. If ∠AOC + ∠BOE = 70° and ∠BOD = 40°, find ∠BOE and reflex ∠COE.
- In Fig. 6.15, ∠PQR = ∠PRQ then prove that ∠PQS = ∠PRT.
- In Fig. 6.16, if x + y = w + z, then prove that AOB is a line.
- In Fig. 6.17, POQ is a line. Ray OR, is perpendicular to line PQ. OS another ray lying between rays OP and OR. Prove that ∠ROS = 1/2 (∠QOS - ∠POS).