SSC CHSL 15 Oct 2020 Shift 1 Paper

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Question : 70 of 100

Marks: +1, -0

In a

\Δ\ABC, \∠\ABC=2 \∠\CAB

, if the side BC is extended to D and

\∠\ACD=126°

, then

\∠\CAB

is

$84°$
$36°$
$42°$
$63°$

Solution:

Given,

Let

\∠\CAB

be

x

.
Given,

\∠\ABC=2 \∠\CAB

∴

\∠\ABC=2 x

In

\Δ\ABC, \∠\ACD

is the exterior angle at point C which is equal to the sum of the interior angles at points A and B.

\∠\ABC+\∠\CAB=\∠\ACD

⇒

2 x+x=126°

⇒

3 x=126°

⇒

x={126}/{3}=42°

⇒

\∠\CAB=42°

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