Question

In ∆ABC, ∠Α = 100°, AD bisects ∠A and AD ⊥ BC. Then, ∠B is equal to ______.

विकल्प

• 80°

• 20°

• 40°

• 30°

Answer 1

In ∆ABC, ∠Α = 100°, AD bisects ∠A and AD ⊥ BC. Then, ∠B is equal to 40°.

Explanation:

Given, ∠BAD = ∠DAC = 50°  ...[∵ AD bisects ∠A and ∠A = 100°]

And ∠BDA = ∠ADC = 90°  ...[∵  AD ⊥ BC]

Now, in ∆ABD,

∠ABD + ∠BAD + ∠BDA = 180°  ...[Angle sum property of a triangle]

⇒ ∠ABD + 50° + 90° = 180°

⇒ ∠ABD + 140° = 180°

⇒ ∠ABD = 180° – 140°

⇒ ∠ABD = 40°