Question

In the figure given below, $O$ is the centre of circle and $\angle AQR=35°$ and $\angle PAQ=120°$ then $\angle SPR$ is equal to:

• A. $35°$
• B. $20°$
• C. $30°$
• D. $25°$

Answer 1

The correct option is A

$35°$

Step 1 Write down the given data.

As per the figure given in the question,

Join SP to obtain the figure.

Here $\angle SPR$ and $\angle SQR$ are angles under the same arc $SR$.

Step 2: Apply Theorem related to Circle.

As angles subtended by the same arc of a circle are equal.

So, $\angle SPR$ and $\angle SQR$ must be equal.

Since,

$$\begin{gathered} \angle SQR=35° \\ \Rightarrow \angle SPR=35° \end{gathered}$$

Hence, option (A) is the correct choice.