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PQRS is a parallelogram such that $∠ Q P S = 75 °$ and $∠ R Q S = 60 °$ . Then find the value of $∠ Q S R$ .

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60°

45°

90°

70°

answer is B.

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Detailed Solution

Given PQRS is a parallelogram such that

∠ Q P S = 75 °

and

∠ R Q S = 60 °

.
We know that the opposite angles of a parallelogram are equal.

∠ S P Q = ∠ Q R S = 75 °

Also, sum of all the angles in a triangle is

180 °

.
Therefore,

∠ S Q R + ∠ Q S R + ∠ S R Q = 180 °

.
Now, substituting the value of

∠ S Q R

and

∠ S R Q

in the above equation we get,

60 ° + ∠ Q S R + 75 ° = 180 °

∠ Q S R + 135 ° = 180 ° ∠ Q S R = 180 ° − 135 ° ∠ Q S R = 45 °

So, the measure of

∠ Q S R

is 45°.
Hence, option 2 is the correct choice.

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