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Question
In ∆ABC, ∠Α = 100°, AD bisects ∠A and AD ⊥ BC. Then, ∠B is equal to ______.
Options
80°
20°
40°
30°
Solution
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 ∆ABC,
∠ABD + ∠BAD + ∠BDA = 180° ......[Angle sum property of a triangle]
⇒ ∠ABD + 50° + 90° = 180°
⇒ ∠ABD + 140° = 180°
⇒ ∠ABD = 180° – 140°
⇒ ∠ABD = 40°
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