Question

in the diagram shown below, rq bisects ∠prs. the measures of the two congruent angles are (x + 40)° and (3x - 20)°. solve for m∠prs. 70° 90° 140° clear all

Explanation:

Step1: Set up the equation

Since RQ bisects ∠PRS, the two congruent - angle measures are equal. So we set up the equation $x + 40=3x - 20$.

Step2: Solve for x

Subtract x from both sides: $40 = 3x - x-20$, which simplifies to $40 = 2x - 20$. Then add 20 to both sides: $40 + 20=2x$, so $60 = 2x$. Divide both sides by 2: $x = 30$.

Step3: Find the measure of one of the congruent angles

Substitute x = 30 into either $x + 40$ or $3x - 20$. Using $x + 40$, we get $30+40 = 70^{\circ}$.

Step4: Find the measure of ∠PRS

Since ∠PRS is composed of two congruent angles, $m\angle PRS=2\times70^{\circ}=140^{\circ}$.

Answer:

$140^{\circ}$