By applying the angle bisector theorem, the measure of angle QPR is equal to 25°.
In Mathematics and Euclidean Geometry, an angle bisector is a type of line, ray, or segment, that typically divides or bisects a line segment exactly into two (2) equal and congruent angles.
Based on the definition of angle bisector, we can logically deduce that angle GFH is congruent with angle EFH;
m∠QPS = m∠RPS + m∠QPR
By using the substitution method, we have:
40 = 8x + 7 + 9x + 16
40 = 17x + 23
17x = 40 - 23
x = 17/17
x = 1
For the measure of angle QPR, we have;
m∠QPR = 9x + 16
m∠QPR = 9(1) + 16
m∠QPR = 25°