Question

In triangle PQR and triangle RST, where PQR and RST have a common vertex R, the points Q, R, and T are collinear and the points P, R, and S are collinear. Side PR is congruent to side QR and side RT is congruent to side ST. The measure of angle STR is 44 degrees. What is the measure of angle QPR?

Answer 1

The measure of angle QPR is 68 degrees.

Step-by-step explanation:

To find the measure of angle QPR, we can use the fact that side PR is congruent to side QR. This means that triangle PQR is an isosceles triangle. In an isosceles triangle, the angles opposite the congruent sides are congruent. So, angle QPR is equal to angle PQR. Since the sum of the angles in a triangle is 180 degrees, we can use this information to find the measure of angle QPR.

Let's assume the measure of angle PQR is x degrees. Since angle QPR and angle PQR are congruent, angle QPR is also x degrees. Since the sum of the angles in triangle PQR is 180 degrees, we can set up the equation:

x + x + 44 = 180

2x + 44 = 180

2x = 136

x = 68

Therefore, the measure of angle QPR is 68 degrees.