Based on the given information, the measure of arc PQ is 168 degrees. Hence, the answer is B none of these.
How to find the measure of the arc
In a circle, the measure of an inscribed angle is equal to half the measure of its intercepted arc.
Given that angle P in triangle PQR is 84 degrees and arc PR is 90 degrees, we can find the measure of arc PQ.
Since angle P is an inscribed angle, the measure of arc PQ will be twice the measure of angle P.
Measure of arc PQ = 2 * Measure of angle P
Measure of arc PQ = 2 * 84 degrees
Measure of arc PQ = 168 degrees
Therefore, the measure of arc PQ is 168 degrees.
The answer is option B. None of these