Explanation

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 = 144^o/2=72^o ∠SRP = ∠PQR (angle formed by a tangent and chord is equal to the angle in the alternate segment) ∴ ∠PQR = 72^o

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 = 144^o/2=72^o ∠SRP = ∠PQR (angle formed by a tangent and chord is equal to the angle in the alternate segment) ∴ ∠PQR = 72^o