Question

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Answer 1

Prove that sum of all three angles is 180° or 2 right angles.

Given: ∆ABC

To prove: ∠A + ∠B + ∠C = 180°

Construction: Draw PQ || BC, passes through point A.

Angle-Sum-Property-of-a-Triangle-theorem-1

Proof: ∠1 = ∠B and ∠3 = ∠C ……. (i)

[∵ alternate angles ∵ PQ || BC]

∵ PAQ is a line

∴∠1 + ∠2 + ∠3 = 180° (linear pair application)

∠B + ∠2 + ∠C = 180°

∠B + ∠CAB + ∠C = 180°

= 2 right angles.

Proved.

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