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In δAbc, If ∠A = 100°, Ad Bisects ∠A and Ad ⊥ Bc. Then, ∠B = - Mathematics

MCQ

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°

  Is there an error in this question or solution?
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APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 11 Triangle and its Angles
Q 9 | Page 25
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