Question

In the figure given below $PQRS$ is a square and $\Delta QTR$ is an equilateral triangle. Find $\angle QMR$

• A. ${45}^o$
• B. ${30}^o$
• C. ${75}^o$
• D. ${60}^o$
• E. $Noneofthese$

Answer 1

The correct option is C ${75}^o$

$PQRS$ is a square

$△QTR$ is equilateral triangle.

$\angle RTQ=\angle TQR=\angle QRT={60}^{\circ }$ ($\because QTR$ is equilateral triangle)

$\angle QSR={45}^{\circ }$ ($\because QS$ is diagonal of square $PQRS$)

In $△QRS$

$\angle SQR={180}^{\circ }-({90}^{\circ }+{45}^{\circ })={45}^{\circ }$

$In△QMR:\angle QRM={60}^{\circ },\angle MQR={45}^{\circ }\therefore QMR={180}^{\circ }-({60}^{\circ }+{45}^{\circ })={75}^{\circ }$