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

2 thoughts on “90°<br />and a:b = 2 : 3,<br />In the given figure, lines XY and MN intersect at O. IfZ POY =<br />find c.<br />​”

1. 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..

   Always stay safe and stay healthy..

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2. 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

   ∘

   Reply