Question

In ABC, BC is produced to D such that exterior angle ACD is formed. Also AB=AC. Find the measure of angle A.​

Answer 1

In ABC, BC is produced to D such that exterior angle ACD is formed. Also AB=AC. Find the measure of angle A.

Given:

In Δ ABC,

AB = AC

BC is produced to D such that ∠ACD = 100°

To find:

The measure of ∠A

Solution:

It is given that,

AB = AC

∴ ∠ABC = ∠ACB ....... [Angles opposite to equal sides are also equal in length] ...... (i)

We have,

∠ACD + ∠ACB = 180° ..... [Linear Pair]

⇒ 100° + ∠ACB = 180°

⇒ ∠ACB = 180° - 100°

⇒ ∠ACB = 80° ..... (ii)

From (i) & (ii), we get

∠ABC = ∠ACB = 80°

Now,

∠ABC + ∠ACB + ∠A = 180° ..... [Sum of the 3 interior angles of a triangle is 180°]

substituting the values of ∠ABC & ∠ACB, we get

⇒ 80° + 80° + ∠A = 180°

⇒ 160° + ∠A = 180°

⇒ ∠A = 180° - 160°

⇒ ∠A = 20°

Thus, the measure of ∠A is 20°

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