Question

what is ( mangle r )?
( mangle r = square^circ )

Explanation:

Step1: Identify right triangle property

The segment RS passes through the circle's center, so $\angle RQS = 90^\circ$ (angle inscribed in a semicircle is a right angle).

Step2: Sum of triangle angles

The sum of angles in a triangle is $180^\circ$. Let $m\angle R = x$.
$x + 90^\circ + 53^\circ = 180^\circ$

Step3: Solve for $m\angle R$

Calculate $x = 180^\circ - 90^\circ - 53^\circ$
$x = 37^\circ$

Answer:

$37$