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ABC is a triangle. The bisectors of the ...

ABC is a triangle. The bisectors of the internal ∠B and external ∠C intersect at D. If angle ∠BDC=50˙ , then ∠A is

A

`60^@`

B

`120^@`

C

`150^@`

D

`30^@`

Text Solution

Verified by Experts

The correct Answer is:
B
`angleCAB = 30^@`
`:. AB` व्यास है
`:. angleACB = 90^@` (अर्द्धवृत्त का कोण समकोण होता है)
`:. DeltaACB` में
`angleABC = 180 - (angleCAB + angleACB)`
`angleADC = 180^@ - angleABC`
`= 180 - (30 + 90) = 60^@`
ABCD, में
`angleADC + angleABC = 180^@`
`= 180^@ -60^@ = 120^@`
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