Question

90°
and a:b = 2 : 3,
In the given figure, lines XY and MN intersect at O. IfZ POY =
find c.
​

Answer 1

Step-by-step explanation:

In the given figure,

∠POY=90

∘

∠POX+∠POY=180

∘

( Linear pair )

∠POX+90

∘

=180

∘

⇒∠POX=90

∘

a:b=2:3

Let a=2x

∘

and b=3x

∘

∠POX=a+b=5x

90

∘

=5x

⇒x=18

∘

∠MOX=b=3x=54

∘

∠MOX+∠NOX=180

∘

( Linear pair)

b+c=180

∘

54

∘

+c=180

∘

c=180

∘

−54

∘

=126

∘

Answer 2

Step-by-step explanation:

=> ∠XOP + ∠POY = 180⁰ 

∵ straight supplementary 

=> ∠XOP + 90⁰ = 180⁰

∴∠XOP = 180⁰ – 90⁰ = 90⁰ 

=> But, ∠XOP = a + b = 90⁰

=> a : b = 2 : 3 

=> 2 + 3 = 5 

=> Ratio Ratio 5 means 90⁰

=> 2 × 90 / 5 = 2 x 18 = 36⁰

∴ If a = 36⁰ then, ∠b = 54⁰. 

=> ∠XOM = ∠YON = b = 54⁰ (∵ Vertically opposite angles) 

=> ∠XON + ∠YON = 180⁰ (∵ v Straight angle) 

∴ c + 54⁰ = 180⁰

=> c = 180 – 54 

∴ c = 126⁰.

I hope this will help you dear..

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