Question

Jessica went shopping at a mall. She bought some dresses that were packed in a shopping bag. The shopping bag was in the shape of a trapezoid. The measure of ∠OPM is 10 less than three times the measure of ∠PMN. What is the measure of ∠OPM of the shopping bag?

Answer 1

Two angles of the adjacent side of a trapezoid should have a total angle of 180. In You can get this equation:
∠OPM + ∠PMN= 180
∠OPM = 180- ∠PMN

∠OPM = 3(∠PMN) -10
180- ∠PMN= 3∠PMN -10
180+10= 3∠PMN + ∠PMN
4 ∠PMN= 190
∠PMN= 47.5

∠OPM + ∠PMN= 180
∠OPM + 47.5= 180
∠OPM = 180-47.5= 132.5