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Question
In a ΔABC, if AB = AC and BC is produced to D such that ∠ACD = 100°, then ∠A =
Options
20°
40°
60°
80°
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Solution
In the triangle ABC it is given that
AB = AC
∠ACD = 100°
We have to find ∠A
Now ∠ACD + ∠ACB = 180° (linear pair)
SinceAB = AC
So, ∠B = ∠C (by isosceles triangle)
This implies that
∠B =∠C
= 180° - 100
= 80
Now,
∠A + ∠B + ∠C = 180° (Property of triangle)
∠A + 80° + 80° = 180°
∠A = 180° - 160°
∠A = 20°
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