In a Δ ABC, if AB = AC and BC is produced to D such that ∠ ACD =100°, then ∠ A =

Question

In a &#x394; ABC, if AB = AC and BC is produced to D such that &#x2220; ACD =100&#xB0;, then &#x2220; A =

Philoid · Accepted Answer

∠ACB + ∠ACD = 180°

On solving we get,

∠ACB = 80°

∠ABC = ∠ACB = 80° (Angles opposite to equal sides are equal)

In ABC,

∠A + ∠B + ∠C= 180°

∠A + 80° + 80° = 180°

∠A = 20°