Question

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:

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

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ANSWER

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

ANSWER

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