Question

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

Answer 1

Step-by-step explanation:

Let ABC be an isosceles triangle with base BC and equal sides AB and AC.

Then, ∠ABC=∠ACB i.e., ∠B=∠C.

Now,

∠ADB+∠ABC=180∘ and ∠ACB+∠ACE=180∘

⇒∠ADB=180∘−∠B and ∠ACE=180∘−∠C

⇒∠ADB=180∘−∠B and ∠ACE=180∘−∠B

⇒∠ADB=∠ACE

Answer 2

Step-by-step explanation:

Let ABC be an isosceles triangle with base BC and equal sides AB and AC.

Then, ∠ABC=∠ACB i.e., ∠B=∠C.

Now,

∠ADB+∠ABC=180°

and ∠ACB+∠ACE=180°

⇒∠ADB=180° −∠B and ∠ACE=180° −∠C

⇒∠ADB=180° −∠B and ∠ACE=180° −∠B

⇒∠ADB=∠ACE