Question

In the given figure, PQ is a diameter and chord SR is parallel to PQ. Given that $\angle PQR={58}^{\circ },$ calculate $\angle RPQ.$

• A. $\angle RPQ={32}^{\circ }$
• B. $\angle RPQ={62}^{\circ }$
• C. $\angle RPQ={39}^{\circ }$
• D. $\angle RPQ={82}^{\circ }$

Answer 1

The correct option is A

$\angle RPQ={32}^{\circ }$

Join PR,

$\angle PRQ={90}^{\circ }$ (Angle in a semi - circle)

$\therefore In△PQR,$

$\angle RPQ=180-(90+58)={32}^{\circ }$