In the following figure, find the value of x:

From figure,

△PRS is an isosceles triangle with PR = SR.

∴ ∠S = ∠RPS = 30°.

∠QPS = ∠QPR + ∠RPS = 52° + 30° = 82°.

Since, sum of angles of triangle = 180°.

Considering △PQS we get,

⇒ ∠P + ∠Q + ∠S = 180°

⇒ 82° + x° + 30° = 180°

⇒ x° + 112° = 180°

⇒ x° = 180° - 112° = 68°.

Hence, x = 68°.