Question

In AOPQ, OQ is extended through point Q to point R, mZPQR = (7x – 19)°,m_OPQ = (2x – 3)', and mZQOP = (x + 16)°. Find mZPQR.

Answer 1

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 =