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CBSE Class 9 Mathematics Question 2 of 6

Lines and Angles — Question 4

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Question 4

In Fig. if x + y = w + z, then prove that AOB is a line.

In Fig. if x + y = w + z, then prove that AOB is a line. NCERT Class 9 Mathematics CBSE Solutions.
Answer

We know that,

Sum of all angles round a point is equal to 360°.

⇒ x + y + w + z = 360°

⇒ (x + y) + (w + z) = 360°

As,

x + y = w + z

⇒ (x + y) + (x + y) = 360°

⇒ 2(x + y) = 360°

⇒ (x + y) = 360°2\dfrac{360°}{2} = 180°.

⇒ x + y = 180° and w + z = 180°.

Since the sum of adjacent angles, x and y with OA and OB as the non-common arms is 180° we can say that AOB is a straight line.

Hence, proved that AOB is a straight line.

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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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