We are given a circle with center P. $RQ$ is tangent to the circle at point $Q$. The measure of angle $QPR$ is $67$ degrees. We need to find the measure of angle $PRQ$.

1. Problem Description

We are given a circle with center P. $RQ$ is tangent to the circle at point $Q$. The measure of angle $QPR$ is $67$ degrees. We need to find the measure of angle $PRQ$.

2. Solution Steps

Since $RQ$ is tangent to the circle at $Q$, the radius $PQ$ is perpendicular to the tangent $RQ$ at $Q$. Therefore, angle $PQR$ is a right angle, so $m\angle PQR = 90^\circ$.

Now, consider triangle $PQR$. The sum of the angles in any triangle is $180^\circ$. So, we have

$m\angle PQR + m\angle QPR + m\angle PRQ = 180^\circ$.

We are given $m\angle QPR = 67^\circ$ and we know $m\angle PQR = 90^\circ$. Substituting these values, we get

$90^\circ + 67^\circ + m\angle PRQ = 180^\circ$

$157^\circ + m\angle PRQ = 180^\circ$

$m\angle PRQ = 180^\circ - 157^\circ$

$m\angle PRQ = 23^\circ$

3. Final Answer

The measure of angle $PRQ$ is $23$ degrees.