Question

In the triangle ABC angle ABC and angle ACB are equal and BC is produced both ways ,prove that the exterior angles are equal​

Answer 1

Step-by-step explanation:

Proof angle ABD and angle ACE are the exterior angles.

angle ABD + angle ABC = 180 (Linear Pair)

angle ABD = 180 - angle ABC

&

angle ACE + angle ACB = 180 (Linear Pair)

angle ACE = 180 - angle ACB ...(i)

As angle ABC and angle ACB are equal.

So, angle ABD = 180 - angle ACB ...(ii)

Therefore, from (i) and (ii) we can say that

angle ABD = angle ACE

Hence Proved.