Question

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
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page 14 of 15

Answer 1

To find the measure of ∠P in triangle ΔOPQ, we can use the fact that the sum of the angles in a triangle is always 180 degrees.

We know that:
- ∠T = 44 degrees
- ∠R = 26 degrees

The angles of triangle ΔRST are given as follows:
- ∠R + ∠S + ∠T = 180 degrees

Substituting the known values:
- 26 + ∠S + 44 = 180
- ∠S + 70 = 180
- ∠S = 180 - 70
- ∠S = 110 degrees

Since ΔOPQ is congruent to ΔRST, the corresponding angles are also congruent:
- ∠P corresponds to ∠S.

Thus, ∠P = ∠S = 110 degrees.

Therefore, the measure of ∠P is **110 degrees**.