Question

Triangle OPQ is congruent to Triangle RST by sss. angle T = 44 degrees, and angle R = 26 degrees. what is the measure of angle P

Answer 1

Since triangles OPQ and RST are congruent, the corresponding angles are also equal.

We are given the measurements for angles \( R \) and \( T \) in triangle RST:
- \( \angle R = 26^\circ \)
- \( \angle T = 44^\circ \)

To find the measure of angle \( S \) in triangle RST, we can use the fact that the sum of the angles in a triangle is \( 180^\circ \):

\[
\angle R + \angle T + \angle S = 180^\circ
\]

Substituting the known values:

\[
26^\circ + 44^\circ + \angle S = 180^\circ
\]

Calculating the sum of angles \( R \) and \( T \):

\[
70^\circ + \angle S = 180^\circ
\]

Now, solving for \( \angle S \):

\[
\angle S = 180^\circ - 70^\circ = 110^\circ
\]

Now, since triangle OPQ is congruent to triangle RST, the corresponding angle \( P \) in triangle OPQ will be equal to angle \( S \):

\[
\angle P = \angle S = 110^\circ
\]

Therefore, the measure of angle \( P \) is \( \boxed{110^\circ} \).