SSC CGL 24 Aug 2021 Shift 2 Paper

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Question : 67 of 100

Marks: +1, -0

Points

A, B

and

C

are on a circle with centre

O

such that

∠ B O C=84^{∘}

. If

A C

is produced to a point

D

such that

∠ B D C=40^{∘}

, then find the measure of

∠ A B D

(in degrees).

98
92
56
102

Solution:

We know that,

∠ B A C=\;{B O C}/{2}

∠ B A C=\;{84}/{2}=42^{∘}

∠ A B D+∠ B D A+∠ D A B=180^{∘}

⇒ \;\; ∠ A B D+40^{∘}+42^{∘}=180^{∘}

⇒ \;\; ∠ A B D=180^{∘}-82^{∘}

∠ A B D=98^{∘}

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