Question

What is the measure of angle PMN? (Image included)

Answer 1

A quadrilateral QNML is a trapezoid, therefore |∡QNM| + |∡NML| = 180°

|∡NML| = 180° - |∡QNM| ⇒ |∡NML| = 180° - 82° = 98°

|∡NML| = |∡NMP| + |∡PML| ⇒ |∡NMP| = |∡NML| - |∡PML|

|∡NMP| = 98° - 30° = 68°

Answer: |∡NMP| = 68° .