Use the image to answer the question.

An illustration shows two congruent triangles in different orientations. Three corresponding sides are marked as congruent.

ΔOPQ≅ΔRST
by SSS. ∠T=44
degrees, and ∠R=26
degrees. What is the measure of ∠P
?

(1 point)
degrees

1 answer

To find the measure of angle \( \angle P \) in triangle \( \Delta OPQ \), we start by using the fact that the sum of angles in a triangle is \( 180^\circ \).

We know:

  • \( \angle T = 44^\circ \)
  • \( \angle R = 26^\circ \)

Since the triangles \( \Delta OPQ \) and \( \Delta RST \) are congruent, corresponding angles are equal. Thus, we can use the measures of angles \( \angle R \) and \( \angle T \) to find \( \angle P \).

  1. First, calculate the measure of \( \angle S \): \[ \angle S = 180^\circ - \angle R - \angle T \] \[ \angle S = 180^\circ - 26^\circ - 44^\circ = 110^\circ \]

  2. Since \( \angle S \) corresponds to \( \angle P \) in \( \Delta OPQ \), we have: \[ \angle P = \angle S = 110^\circ \]

Thus, the measure of \( \angle P \) is \( 110 \) degrees.