Answer:
m∠QPR = 20°
Step-by-step explanation:
If we make a sketch of the triangle, it will be observed, that line R bisects angle P.
Considering Triangle, ΔQPS;
∠QPS=107∘
Considering triangle, QPR;
∠QPR=9x-115∘
Considering triangle, RPS;
∠RPS=4x+27∘
Thus, ∠RPS + ∠QPR = ∠QPS
4x+27° + 9x-115° = 107°
13x - 88° = 107∘
13 x = 107∘ + 88∘
13x = 195°
x = 195°/13
x = 15°
m∠QPR = 9x - 115°
= (9 x 15) - 115°
= 135° - 115°
= 20°
Therefore, m∠QPR = 20°
