In a Δ ABC, if AB = AC and BC is produced to D such that ∠ACD =100°, then ∠A =
A. 20°
B. 40°
C. 60°
D. 80°
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Answer:
Your answer is here A) 20
Answered by
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Given : In a Δ ABC, if AB = AC and BC is produced to D such that ∠ACD = 100°.
∠ACB + ∠ACD = 180°
[Linear pair]
∠ACB + 100° = 180°
∠ACB = 180° - 100°
∠ACB = 80°
∠ABC = ∠ACB = 80°
[Angles opposite to equal sides are equal]
In ∆ABC,
We know that the sum of the angles of a triangle is 180°
∠A + ∠B + ∠C = 180°
∠A + 80° + 80° = 180°
∠A + 160° = 180°
∠A = 180° - 160°
∠A = 20°
Hence, ∠A is 20°.
Option (A) 20° is correct.
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