SSC CHSL 13 Apr 2021 Shift 3 Paper

Section: Quantitative Aptitude

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Question : 52 of 100

Marks: +1, -0

The side

B C

of a

△ A B C

is extended to a point

D

. If

∠ A C D=117^{∘}

and

∠ A B C=\;{5}/{8} ∠ B A C

, then what is the measure of

∠ A B C

?

$45^{∘}$
$72^{∘}$
$36^{∘}$
$54^{∘}$

Solution:

Given,

Let

\;\; ∠ B A C=x

Then,

∠ A B C=\;{5}/{8} x

By external angle property,

∠ A C D=∠ C A B+∠ A B C

⇒ \;\; x+\;{5}/{8} x=117

⇒ \;\; \;{8 x+5 x}/{8}=117

⇒ \;\; \;{13 x}/{8}=117

⇒ \;\; x=\;{117 × 8}/{13}=72^{∘}

∴ \;\; ∠ A B C=\;{5}/{8} x=\;{5}/{8} × 72=45^{∘}

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