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Prove that exterior angle of a …

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Prove that exterior angle of a triangle is equal to the sum of its interior opposite angles

Posted by Pragya Ahuja 5 years, 9 months ago

CBSE > Class 07 > Mathematics

1 answers

Yogita Ingle 5 years, 9 months ago

An exterior angle of a triangle is equal to the sum of its interior opposite angles.

Consider triangle ABC. ∠ACD is an exterior angle.

Through C, draw CE||BA

To prove: ∠ 1 + ∠2 = ∠ACD

Proof: ∠1 = ∠x (pair of alternate interior angles since, CE||BA)

∠2 = ∠y (pair of corresponding angles)

∠1 + ∠2 = ∠x + ∠y

i.e. ∠1 + ∠2 = ∠ACD [ ∠x + ∠y = ∠ACD]

Hence proved.

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CBSE > Class 07 > Mathematics