Answer:
x = 8
Step-by-step explanation:
m<PQR = (2x + 6)°
m<RPQ = (x - 7)°
m<QRS = (5x - 17)°
<PQR and <RPQ are interior angles opposite to the exterior angle <RPQ.
Therefore,
m<PQR + m<RPQ = m<QRS (Exterior Angle Theorem of a Triangle)
Substitute in the values
2x + 6 + x - 7 = 5x - 17
Add like terms
3x - 1 = 5x - 17
Collect like terms
3x - 5x = 1 - 17
-2x = -16
-2x/-2 = -16/-2
x = 8
