From the diagram, angles OQP and PQR are supplementary, then:
m∠OQP + m∠PQR = 180°
m∠OQP + (7x - 19)° = 180°
m∠OQP = 180 - (7x - 19)
m∠OQP = 180 + 19 - 7x
m∠OQP = 199 - 7x
The addition of the three interior angles of a triangle is equal to 180°, that is:
m∠OQP + m∠OPQ + m∠QOP = 180°
(199 - 7x) + (2x - 3) + (x + 16) = 180
(199 - 3 + 16) + (-7x + 2x + x) = 180
212 - 4x = 180
-4x = 180 - 212
x = (-32)/(-4)
x = 8
And the value of m∠PQR is:
m∠PQR =
