Question

in triangle pqr, shown below, angle p measures 140°. angle q has the same measure as angle r. what is the measure of angle q? \
triangle pqr with angle at p being 140° and angle at q marked with?

Explanation:

Step1: Recall triangle angle sum

The sum of angles in a triangle is $180^\circ$.

Step2: Define variable for angle Q/R

Let $m\angle Q = m\angle R = x$.

Step3: Set up angle sum equation

$$140^\circ + x + x = 180^\circ$$

Step4: Simplify and solve for x

$$140^\circ + 2x = 180^\circ$$
$$2x = 180^\circ - 140^\circ = 40^\circ$$
$$x = \frac{40^\circ}{2} = 20^\circ$$

Answer:

$20^\circ$