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CBSE Class 9 Mathematics Question 2 of 11

Lines and Angles — Question 2

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Question 2

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

In Fig. lines XY and MN intersect at O. If ∠POY = 90° and a : b = 2 : 3, find c. NCERT Class 9 Mathematics CBSE Solutions.
Answer

Since,

∠POY = 90°

Line OP is perpendicular to line XY. Hence ∠POY = ∠POX = 90°

Given, a : b = 2 : 3

Let a = 2x and b = 3x, where x is some number.

From figure,

⇒ ∠POX + ∠POY = 180° (Linear pairs)

⇒ ∠POM + ∠MOX + ∠POY = 180°

⇒ a + b + 90° = 180°

⇒ 2x + 3x = 180° - 90°

⇒ 5x = 90°

⇒ x = 90°5\dfrac{90°}{5}

⇒ x = 18°.

⇒ a = 2x = 2(18°) = 36°

⇒ b = 3x = 3(18°) = 54°

Since MN is a straight line,

⇒ ∠MOX + ∠XON = 180° (Linear pairs)

⇒ b + c = 180°

⇒ 54° + c = 180°

⇒ c = 180° - 54°

⇒ c = 126°.

Hence, c = 126°.