If the base of an isosceles triangle is produced on both sides, prove that the exterior angles so formed are equal to each other.

Question

Philoid · Accepted Answer

To prove: the exterior angles formed are equal to each other

i.e., ∠ADB =∠ACE

Proof: Let ABC be an isosceles triangle

Where BC is the base of the triangle and AB and AC are its equal sides.

∠ABC =∠ACB

∠B =∠C (Angle opposite to equal sides)

Now,

∠ADB +∠ABC = 180°

∠ACB +∠ACE =180°

∠ADB =180° -∠B

And

∠ACE=180°-∠C

∠ADB = 180° - ∠B

And

∠ACE=180°-∠B

∠ADB =∠ACE

Hence, proved