PQ and RS are two chords of a circle. PR and QS meets at T when produced. If PQ is the longest chord of circle and ∠PTQ= 72°, then find the value of ∠ROS?

PQ is the longest chord, so it's the diameter. Angle PTQ = 72° is in the semicircle (exterior point T). Using the property: angle subtended by arc at any point on circumference = half the angle at center. Arc PQ subtends 72° at T, so angle PRQ = 72°. At center O, angle ROS subtended by same arc RS = 2 × angle subtended at circumference = 2 × 18° = 36°.