We are given a circle with intersecting chords $SP$ and $TR$. The measure of angle $SUT$ is $47^\circ$ and the measure of arc $ST$ is $53^\circ$. We are asked to find the measure of arc $PR$.

1. Problem Description

We are given a circle with intersecting chords $SP$ and $TR$. The measure of angle $SUT$ is $47^\circ$ and the measure of arc $ST$ is $53^\circ$. We are asked to find the measure of arc $PR$.

2. Solution Steps

The measure of an angle formed by two chords intersecting inside a circle is half the sum of the intercepted arcs.

In our case, $\angle SUT = 47^\circ$ and it intercepts arcs $ST$ and $PR$.

So,

$m\angle SUT = \frac{1}{2}(m\stackrel{\frown}{ST} + m\stackrel{\frown}{PR})$

$47^\circ = \frac{1}{2}(53^\circ + m\stackrel{\frown}{PR})$

Multiply both sides by 2:

$94^\circ = 53^\circ + m\stackrel{\frown}{PR}$

Subtract $53^\circ$ from both sides:

$m\stackrel{\frown}{PR} = 94^\circ - 53^\circ$

$m\stackrel{\frown}{PR} = 41^\circ$

3. Final Answer

$m\stackrel{\frown}{PR} = 41^\circ$