Math, asked by saicharan312008, 1 month ago

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

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Answers

Answered by serenealmeida
0

Answer:

30,45,135

Step-by-step explanation:

since <POY = 90°

<POX= 90°

<POX= <POM+<MOX

90= 2x+3x

90= 6x

x= 15

a:2x= 30 °

b: 3x= 45 °

<MOX + <XON =180° .. linear pair

45 + c= 180

c= 135°

Answered by moonsarkar947
2

Answer:

C =126°

Step-by-step explanation:

Given:

∠POY= 90° and a : b = 2 : 3

To find:

C

Solution:

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°

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