Congruency of Triangles Practice

Question

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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)

Answer 1

To find the measure of angle \( \angle P \) in triangle \( \Delta OPQ \), we can use the property that the sum of the angles in a triangle is always 180 degrees.

We know:

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

First, we can find the measure of angle \( \angle S \) in triangle \( \Delta RST \):

\[ \angle S = 180^\circ - (\angle R + \angle T) = 180^\circ - (26^\circ + 44^\circ) = 180^\circ - 70^\circ = 110^\circ \]

Since the triangles are congruent (\( \Delta OPQ \cong \Delta RST \)), the corresponding angles are also congruent. Thus, we have:

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

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