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Question
In ΔABC, if ∠A = 100°, AD bisects ∠A and AD ⊥ BC. Then, ∠B =
Options
50°
90°
40°
100°
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Solution
In the given ΔABC, ∠A= 100°, AD bisects ∠Aand AD ⊥ BC.
Here, we need to find ∠B.
As, AD bisects∠A,
We get,
∠BAD = ∠DAC
100 = 2∠BAD
∠BAD = 50°
Now, according to angle sum property of the triangle
In ΔABD
∠A + ∠B + ∠D = 180°
50° + ∠B + 90° = 180°
140° + ∠B = 180°
∠B = 180° - 140°
= 40°
Hence, ∠B = 40°
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