Question

State and prove exterior angle of a triangle property with a example .

Answer 1

Answer:

If any side of a triangle is extended, then the exterior angle so formed is the sum of the two opposite interior angles of the triangle. In the given figure, the side BC of ∆ABC is extended. The exterior angle ∠ACD so formed is the sum of measures of ∠ABC and ∠CAB.

Answer 2

Answer:

AN EXTERIOR ANGLE OF A TRIANGLE IS EQUAL TO THE SUM OF 2 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.