In the figure given below, $O$ is the centre of the circle and $S P$ is a tangent. If $∠ S R T = 65^{o}$ , find the value of $x$ , $y$ and $z$ .

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Solution

In $△ O S P$ , $∠ O S R = 90^{o}$ [Radius is perpendicular to tangent]
In $△ T S R$
$x + 90^{o} + 65^{o} = 180^{o}$
$∴$ $x = 25^{o}$
$∠ S O Q = 2 ∠ S T R$
[Angle at centre $= 2 \times$ Angle at circumference]
$y = 2 \times 25 = 50^{o}$
In $△ O S P$ ,
$50^{o} + 90^{o} + z = 180^{o}$
$∴$ $z = 40^{o}$

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