Question

What is the measure of? angle PQR [Not drawn to scale) -51 -55 -74 -78

Answer 1

Given:

The exterior angle P is 74°

The measure of ∠PRQ is 51°

We need to determine the measure of ∠PQR

Measure of ∠QPR:

From the figure, it is obvious that P is the intersection of the two lines.

The angle 74° and ∠QPR are vertically opposite angles.

Since, vertically opposite angles are always equal, then the measure of ∠QPR is 74°

Thus, the measure of ∠QPR is 74°

Measure of ∠PQR:

The measure of ∠PQR can be determined using the triangle sum property.

Thus, we have;

$\angle PQR+\angle QPR+\angle PRQ=180^{\circ}$

Substituting the values, we get;

$\angle PQR+74^{\circ}+51^{\circ}=180^{\circ}$

       $\angle PQR+125^{\circ}=180^{\circ}$

                  $\angle PQR=55^{\circ}$

Thus, the measure of ∠PQR is 55°

Hence, Option B is the correct answer.

Answer 2

Answer:

Step-by-step explanation: