Final answer:
To find the measure of ∠PQR, one must first solve for x by equating the sum of the measures of ∠RQT and ∠PQT, and then doubling the measure of one of the bisected angles.
Step-by-step explanation:
To determine the measure of ∠PQR when Ray QT bisects ∠PQR, sum the measures of ∠RQT and ∠PQT. Given that the measure of ∠RQT is (5x+14)° and the measure of ∠PQT is (8x-4)°, the equation to find the value of x is (5x+14)+(8x-4) = (5x+8x)+(14-4), which simplifies to 13x+10. Next, the measure of ∠PQR is twice the measure of one of its bisected angles, so m∠PQR = 2*(5x+14). Substituting the x found from the equation will give us the measure of ∠PQR.