# 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°

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