In the figure, PQ and XY are parallel tangents. If ∠QRT = 30°, then find the value of ∠TSY.

In the given figure,

Let O be the centre of the circle

Join OS

Let O be the centre of the circle

So ∠ SRQ = 90° [radius is perpendicular to tangent]

So ∠ SRT = 90 – 30

= 60°

∠ STR = 90° [angle in a semicircle is 90°]

∠ RSY = 90° [radius is perpendicular to tangent]

∠ RST + ∠ STR + ∠ SRT = 180° [sum of internal angles in a triangle is 180°]

∠ RST + 90 + 60 = 180

∠ RST = 180 – 150

∠ RST = 30°

∠ TSY = ∠ RSY - ∠ RST

= 90 – 30

= 60°

∴ ∠ TSY = 60°