SSC CGL 23 Aug 2021 Shift 2 Paper

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Question : 67 of 100

Marks: +1, -0

In

△ A B C, D

is a point on

B C

such that

∠ B A D=\;{1}/{2} ∠ A D C, ∠ B A C=77^{∘}

and

∠ C=45^{∘}

. What is the measure of

∠ A D B

?

$77^{∘}$
$64^{∘}$
$58^{∘}$
$45^{∘}$

Solution:

Given,

∠ B A D=\;{1}/{2} ∠ A D C

,

∠ B A C=77^{∘}, ∠ C=45^{∘}

∠ A D B=

?
We know that,

∠ A+∠ B=∠ A D C

[Exterior angle property]

⇒ \;\; x+∠ B=2 x

⇒ \;\; ∠ B=x

In

△ A B C

,

∠ A+∠ B+∠ C=180^{∘}

⇒ 77^{∘}+∠ B+45^{∘}=180^{∘}

⇒ ∠ B=180^{∘}-(77^{∘}+45^{∘})

=(180^{∘}-122)^{∘}=58^{∘}

⇒ \;\; ∠ B=58^{∘}=x

Now,

∠ B D C=∠ A D B+∠ A D C

[ ∵

Linear angle

]

⇒ \;\; 180^{∘}=∠ A D B+2 × 58^{∘}

⇒ \;\; ∠ A D B=180^{∘}-116^{∘}=64^{∘}

∴ \;\; ∠ A D B=64^{∘}

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