Question

In Fig. 6.14, lines XY and MN intersect at O. If ZPOY =90° and a:b=2:3, find c.​

Answer 1

Step-by-step explanation:

Given: ∠POY= 90° and a : b = 2 : 3.

If two lines intersect with each other, then the vertically opposite angles formed are equal.

In Fig. 6.14, lines XY and MN intersect at O. If ∠POY = 90° and a : b = 2 : 3, find c.

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°

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Answer 2

Answer:

126°

Step-by-step explanation:

a° + b° = 90°

Given that the ratio is 2:3 let a and b be 2x and 3x respectively,

Then,

2x + 3x = 90°

5x = 90°

x = 90°/5

x = 18°

a = 2x = 2 × 18° = 36°

b = 3x = 2 × 18° = 54°

a° + p° + o° = b° + c° = 180°

54° + c° = 180°

c° = 180° - 54°

c° = 126°