Question

find value of x




pls answer fast. ​

Answer 1

Given that,

$\sf{\angle POR = {140}^{\degree}}$

We observed,

$\sf{\angle PSR = \frac{1}{2} \angle POR}$

[As, angle subtended by a chord 'PR' at the centre is double the value of any angle subtended by it in the boundary of the circle.]

$\sf{\implies \angle PSR = \frac{1}{2} ({140}^{\degree}) }$

$\sf{\implies \angle PSR = {70}^{\degree}}$

We also know that,

Sum of opposite interior angles of a cyclic quadrilateral is equal to 180°.

$\sf{ \angle PXR}$ in terms of $\sf{ (x)}$:-

$\sf{\boxed{\sf{ \angle PSR = 180° - x}}}$

(Both the angles make 180° — Linear Pair)

So,

$\sf{\therefore (180° - x) + 70° = 180°}$

$\sf{\implies x = 70°}$ (Answer)