Question

In the adjoining figure given below, $O$ is the centre of circle, the value of $x$ is:

• A. $80°$
• B. $75°$
• C. $70°$
• D. $65°$

Answer 1

The correct option is C

$70°$

Step 1: Angle sum property of triangle.

Considering the$△RLP$

As we know,

The Sum of all the interior angles of the triangle is $=180°$

$$\begin{gathered} \angle P+\angle RLP+\angle PRL=180° \\ \angle PRL=180°-(70°+90°)=180°-160°=20° \end{gathered}$$

Step 2: Property of semicircle.

As PQ is the diameter

As we know,

The angle subtended by diameter in a semicircle is a right angle$=90°$.

$\therefore \angle PRQ=90°$ (Angle in the semi-circle)

$x=90°-20°=70°$

Hence, option (C) is the correct choice.