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?

Question

Mathematics

Ronald Anthony

3 July, 15:16

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?

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Nathalia Weeks · 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