Question

2. In Fig. 6.14, lines XY and MN intersect at O. If
Z POY = 90° and a:b= 2:3, find c.
h
O
Y
N'S​

Answer 1

Given:

• a : b = 2 : 3

To Find:

• c

Solution:

Let a = 2x and b = 3x,

where x is some number.

According to the question,

→ ∠POX + ∠POY = 180° [ Linear pair]

→ a + b + 90° = 180°

→ a + b = 180° - 90°

→ 2x + 3x = 90°

→ 5x = 90°

→ x = 90/5

→ x = 18°

Then,

• a = 2x = 2 × 18° = 36°
• b = 3x = 3 × 18° = 54°

We need to find C,

Since MN is a line, we can use linear pair,

→ ∠MOX + ∠XON = 180° [Linear pair]

→ b + c = 180°

→ 54° + c = 180°

→ c = 180° - 54°

→ c = 126°

Hence,

• c = 126°