Question

In the given figure, find the measure of $\angle RQT$ if $PQ=QR$ and $\angle QPR={60}^{\circ }$.

• A. ${60}^{\circ }$
• B. ${140}^{\circ }$
• C. ${120}^{\circ }$
• D. ${100}^{\circ }$

Answer 1

The correct option is C

${120}^{\circ }$

$\Delta PQR$ is isosceles since $PQ=QR$.
$\therefore \angle QPR=\angle QRP={60}^{\circ }$
$\angle RQT$ is the exterior angle of $\Delta PQR$ which is equal to the sum of interior opposite angles $\angle P$ and $\angle R$.
Hence, $\angle RQT={60}^{\circ }+{60}^{\circ }={120}^{\circ }$.