SSC CGL 23 Aug 2021 Shift 1 Paper

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Question : 61 of 100

Marks: +1, -0

Vertices

A, B, C

and

D

of a quadrilateral

A B C D

lie on a circle,

∠ A

is three times

∠ C

and

∠ D

is two times

∠ B

. What is the difference between the measures of

∠ D

and

∠ C

?

$65^{∘}$
$45^{∘}$
$75^{∘}$
$55^{∘}$

Solution:

According to the question,

∠ A

is three times of

∠ C ⇒ ∠ A=3 ∠ C

∠ D

is two times of

∠ B ⇒ ∠ D=∠ B × 2

We know,

∠ A+∠ C=180^{∘}

and

∠ A=3 ∠ C

So,

3 ∠ C+∠ C=180

4 ∠ C=180^{∘}

∠ C=45^{∘}

Similarly,

∠ B+∠ D=180^{∘}

So,

\;\; \;{∠ D}/{2}+∠ D=180

\;{3 ∠ D}/{2}=180^{∘}

[ ∵ ∠ D=2 ∠ B]

∠ D=120^{∘}

Difference between

∠ D

and

∠ C

=120^{∘}-45^{∘}=75^{∘}

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