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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°.

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Mathematics | Lines and AnglesWeb Content • Interactive Notes

Lines and Angles — Interactive Study Guide

Angle Pair Cheat Sheet

PairRelationshipCondition
ComplementarySum = 90°Any two angles
SupplementarySum = 180°Any two angles
Linear PairSum = 180°Adjacent + on a line
Vertically OppositeEqualIntersecting lines
CorrespondingEqualParallel lines + transversal
Alternate InteriorEqualParallel lines + transversal
Co-interiorSum = 180°Parallel lines + transversal

Triangle Angle Facts

∠A + ∠B + ∠C = 180° (angle sum property)
Exterior angle = sum of remote interior angles

Quick Self-Check

  1. Two parallel lines cut by a transversal: one angle is 72°. Find all 8 angles. (72°, 108° alternating)
  2. In ΔABC, ∠A = 45°, ∠B = 65°. Find ∠C. (70°)
  3. An exterior angle of a triangle is 130°. One non-adjacent interior angle is 50°. Find the other. (80°)

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