Step 1:
Concept: Use the two theorems below to find the measure of angle QRS
1. The sum of angles in a triangle is 180 degrees
2. The sum of angles on a straight line is 180 degrees.
Step 2:
Angle QRP is on a straight line with angle QRS = 20x + 12
[tex]\begin{gathered} m\text{QRP + mQRS = 180} \\ m\text{QRP + 20x + 12 = 180} \\ m\text{QRP = 180-12-20x} \\ m\text{QRP = 168 - 20x} \end{gathered}[/tex]
Step 3:
Sum of angles in a triangle = 180
[tex]\begin{gathered} 9x\text{ + 13x + 168 - 20x = 180} \\ \text{Collect similar terms} \\ 9x\text{ + 13x - 20x = 180 - 168} \\ 2x\text{ = 12} \\ \text{x = }\frac{12}{2} \\ \text{x = 6} \end{gathered}[/tex]
Final answer
m
= 20(6) + 12
= 120 + 12
= 132 Option C
