Question

someone solve this please. I have my exams in 1 he please ​

Answer 1

Answer:

x = 105°

y = 45°

Step-by-step explanation:

Since, the given figure is a square. Therefore, ∠SPQ = ∠PQR = ∠QRS = ∠RSP = 90°.

Also, QS is a diagonal of the square PQRS.

Let the point where the line from P makes an angle 60° with QR be T and the point where the diagonal QS meets PT be M.

⇒ ∠QTP = 60° (Given)

w.k.t., diagonal of a square bisect its angle.

⇒ ∠RSQ = ∠PSQ = ∠PQS = ∠RQS = 90°/2 = 45°

So, y = ∠RSQ = 45°

In triangle PQT, by Angle sum property of triangle,

∠TPQ + ∠PQR + ∠QTP = 180°

⇒ ∠TPQ + 90° + 60° = 180°

⇒ ∠TPQ + 150° = 180°

⇒ ∠TPQ = 180° - 150° = 30°

Now, in triangle PQM, by angle sum property of triangle,

∠TPQ + ∠PQS + ∠PMQ = 180°

⇒ 30° + 45° + x = 180°

⇒ x + 75° = 180°

⇒ x = 180° - 75° = 105°