Question

State and prove the “Exterior angle property of a triangle”.​

Answer 1

Answer:

The exterior angle of triangle is equal to interior opposite angle..

Answer 2

Answer:

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

Explanation:

Consider triangle ABC.

∠ACD is an exterior angle.

Through C, draw

CE//BA

image

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.