Question

in △qrs, $overline{qr}congoverline{sq}$ and $mangle s = 66^{circ}$. find $mangle r$.

Explanation:

Step1: Identify isosceles - triangle property

Since $\overline{QR}\cong\overline{SQ}$ in $\triangle QRS$, $\angle R\cong\angle S$.

Step2: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is $180^{\circ}$, so $m\angle Q + m\angle R+m\angle S=180^{\circ}$.

Step3: Substitute the known angle measure

We know $m\angle S = 66^{\circ}$, and since $m\angle R = m\angle S$, then $m\angle R=66^{\circ}$.

Answer:

$66^{\circ}$