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In the given figure, $PQRS$ is a cyclic quadrilateral. Then, which of the following is the measure of $∠ P$ and $∠ Q$ ?

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135^{\circ}, 60^{\circ}

60^{\circ}, 120^{\circ}

60^{\circ}, 90^{\circ}

100^{\circ}, 120^{\circ}

answer is A.

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Detailed Solution

Consider the given question,
Question Image

Here,

P Q RS

is a cyclic quadrilateral.
We know that,
Opposite angles of a cyclic quadrilateral are supplementary.
Then,

∴ 3 x + x = 180^{\circ}

\Rightarrow 4 x = 180^{\circ}

\Rightarrow x = 45^{\circ}

And,

2 y + y = 180^{\circ}

3 y = 180^{\circ}

y = 60^{\circ}

∴ ∠ P = 3 x

∠ P = 3 \times 45^{\circ}

∠ P = 135^{\circ}

and

∠ Q = y = 60^{\circ}

.
Hence, the measure of

∠ P

and

∠ Q

135^{\circ}

and

60^{\circ}

.
Therefore, option 1 is correct.

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