Question

the measure of angle q is 70 degrees.
find the measure of angle p.

Explanation:

To solve for the measure of angle \( P \) in triangle \( PQR \), we assume it is an isosceles right triangle (since \( PR = PQ \) or \( RQ \) is a leg, and \( \angle R \) is a right angle, \( 90^\circ \)) or a right triangle with \( \angle R = 90^\circ \). Wait, actually, looking at the triangle, if \( \angle R \) is a right angle (\( 90^\circ \)) and \( \angle Q = 70^\circ \), then we use the fact that the sum of angles in a triangle is \( 180^\circ \).

Step 1: Recall the triangle angle sum theorem

The sum of the interior angles of a triangle is \( 180^\circ \). So, for triangle \( PQR \), we have:
\[
\angle P + \angle Q + \angle R = 180^\circ
\]

Step 2: Identify the known angles

We know \( \angle Q = 70^\circ \). If \( \angle R \) is a right angle (since the triangle looks like a right triangle at \( R \)), then \( \angle R = 90^\circ \).

Step 3: Solve for \( \angle P \)

Substitute the known values into the angle sum formula:
\[
\angle P + 70^\circ + 90^\circ = 180^\circ
\]
Simplify the left side:
\[
\angle P + 160^\circ = 180^\circ
\]
Subtract \( 160^\circ \) from both sides:
\[
\angle P = 180^\circ - 160^\circ
\]
\[
\angle P = 20^\circ
\]

Answer:

The measure of angle \( P \) is \( \boxed{20^\circ} \).