Question

In the diagram, segment $PQ$ is a tangent to the circle at $P$ and $QRS$ is a straight line. The value of $x$ is

• A. ${25}^o$
• B. ${30}^o$
• C. ${35}^o$
• D. ${40}^o$

Answer 1

The correct option is D ${40}^o$

${180}^o-\angle QPS=\angle PQS+PSQ$
[Exterior angle of a triangle is equal to sum of interior opposite angles]
$={35}^0+x$
$\angle RPQ=\angle PSQ=x^0$
[Angles in the alternate segment]
$\angle TPS+\angle SPR+\angle RPQ={180}^0$
[Linear pair]
$35+x+65+x=180$
$2x=180-100$
$2x=80$
$x^0={40}^0$

Hence, option D.