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PQRS is a rectangle and $∠ P S Q = 35 °$ . Determine $∠ SQR, ∠ S P R, ∠ Q S R$ .

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∠ S Q R = 35 °; ∠ S P R = 35 °; ∠ Q S R = 55 °

∠ S Q R = 65 °; ∠ S P R = 35 °; ∠ Q S R = 55 °

∠ S Q R = 35 °; ∠ S P R = 65 °; ∠ Q S R = 55 °

∠ S Q R = 65 °; ∠ S P R = 45 °; ∠ Q S R = 65 °

answer is A.

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Detailed Solution

Given,
A rectangle PQRS,

∠ P S Q = 35 °

Consider,

∠ S Q R = x, ∠ S P R = y, ∠ Q S R = z

Now, all the angles of rectangle are

90 °

⇒ ∠ P S Q + ∠ Q S R = 90 °

⇒ 35 ° + z = 90 ° ⇒ z = 55 °

Now, the diagonals of the rectangle bisect each other.
⇒SA=RA and PA=QA.
And,

SP = RQ

[Opposite sides of rectangle]
By SSS test,

Δ S P A ≅ Δ R Q A

.
By CPCT,

∠ P S A = ∠ Q R A = 35 ° [Given]

∠ Q R P = ∠ S P R = 35 °

[Alternate angles.]
Now,

∠ S Q R = ∠ P S Q = 35 ° [Alternate angles]

Therefore, the values are

∠ S Q R = 35 °; ∠ S P R = 35 °; ∠ Q S R = 55 °

.
Hence, the correct option is 1.

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