State and prove the exterior angle property of a triangle.

Asked by Topperlearning User | 17th Nov, 2013, 11:17: PM

Expert Answer:

Statement :

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.

Answered by  | 18th Nov, 2013, 01:17: AM