From ∆PSR

|PS| = |SR| (If two tangents are drawn from an external point of the circle, then they are of equal lengths)

∴ ∆PSR is isosceles

∠PSR + ∠SRP + ∠SPR = 180\(^o\) (sum of angles in a triangle)

Since |PS| = |SR|; ∠SRP = ∠SPR

⇒ ∠PSR + ∠SRP + ∠SRP = 180\(^o\)

∠PSR + 2∠SRP = 180\(^o\)

36\(^o\) + 2∠SRP = 180\(^o\)

2∠SRP = 180\(^o\) - 36\(^o\)

2∠SRP = 144\(^o\)

∠SRP = \(\frac {144^o}{2} = 72^0\)

∠SRP = ∠PQR (angle formed by a tangent and chord is equal to the angle in the alternate segment)

∴ ∠PQR = 72\(^0\)