Question

In the figure given below, O is the centre of the circle and SP is a tangent. If ∠SRT = 65°,
find the value of x, y and z.

Answer 1

In the given figure, TS ⊥ SP,

m∠TSR = m∠OSP = 90°

In `triangle TSR, m angleTSR + m angleTSR + m angle RTS = 180^@`

`=> 90^@ + 65^@ + x = 180^@`

`=> x = 180^@ - 90^@ - 65^@`

`=> x= 25^@`

Now, y = 2x [Angle subtended at the centre is double that of the angle subtended by the arc at the same centre]

`=> y = 2 xx 25^@`

`:. y = 50^@`

In `triangle OSP ,m angleOSP + m angle SPO + m angle POS    =180^@`

`=> 90^@ + z + 50^@ = 180^@`

`=> z = 180^@ - 140^@`

`:. z=40^@`