Question

In the figure given below, PQRS is a square and triangle TSR is an equlilateral triangle. What is the measure of $x$?

• A. 45°
• B. 30°
• C. 40°
• D. 60°

Answer 1

The correct option is A 45°

Given,
Quadrilateral PQRS is a square,
$\therefore PQ=QR=RS=SP$
And, all the interior angles measure 90°

Also, the triangle TSR is an equilateral triangle,
$\therefore TS=SR=RT$
$\angle TSR=\angle SRT=\angle RTS=60°$
In triangle QRT,
$\angle QRT=\angle QRS+\angle SRT$
$\Rightarrow \angle QRT=90°+60°=150°$

Since, triangle QRT is an isoceles triangle
$\angle RTQ=\angle TQR$
$\therefore \angle RTQ=\frac{180°-150°}{2}=15°$

We know that,
$\angle RTS=60°$
$or\angle RTS=\angle RTQ+\angle QTS$
$\Rightarrow 60°=x°+15°$
$\Rightarrow x°=60°-15°=45°$