MathematicsIn the given figure, PQRS is a cyclic quadrilateral. Its diagonals PR and QS intersect each other at T. If ∠PRS=80∘ and ∠RQS=50∘. Which of the following is the measure of ∠PSR?

In the given figure, $PQRS$ is a cyclic quadrilateral. Its diagonals $PR$ and $QS$ intersect each other at $T$ . If $∠ PRS = 80^{\circ}$ and $∠ RQS = 50^{\circ}$ . Which of the following is the measure of $∠ PSR$ ?

A
$30^{\circ}$
B
$50^{\circ}$
C
$70^{\circ}$
D
$90^{\circ}$

Solution:

Consider the given figure,

It is given that

PQRS

is a cyclic quadrilateral.

∠ PRS = 80^{o}

∠ RQS = 50^{o}

Angles in the same segment are equal.
Then,

∠ RQS = ∠ RPS

.
In

△ PSR

, by angle sum property,

∠ PRS + ∠ RPS + ∠ PSR = 180^{o}

80^{o} + 50^{o} + ∠ PSR = 180^{o}

130^{o} + ∠ PSR = 180^{o}

\Rightarrow ∠ PSR = 180^{o} - 130^{o}

\Rightarrow ∠ PSR = 50^{o}

Hence, the measure of

∠ PSR

50^{o}

.
Therefore, option 2 is correct.

In the given figure, $PQRS$ is a cyclic quadrilateral. Its diagonals $PR$ and $QS$ intersect each other at $T$ . If $∠ PRS = 80^{\circ}$ and $∠ RQS = 50^{\circ}$ . Which of the following is the measure of $∠ PSR$ ?

Solution:

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