In trapezoid MNPQ shown below, MN QP,. 108 m M. ∠ = ,. 4 15 m P x. ∠ = - , and. 3 21 m Q x. ∠ = + . Explain why m N. ∠ must be 127

The answer is below

Step-by-step explanation:

A trapezoid is a quadrilateral (has four sides and four angles) with a pair of opposite parallel sides. The pair of opposite parallel side is known as the base. Also, the angles on the same leg of a trapezoid (adjacent angles) are supplementary (add up to 180°).

In trapezoid MNPQ:

∠M + ∠Q = 180° (angles on the same leg are supplementary)

108 + (3x + 21) = 180

3x + 129 = 180

3x = 51

x = 17

Also:

∠N + ∠P = 180° (angles on the same leg are supplementary)

∠N + (4x - 15) = 180

∠N = 180 - (4x - 15)

∠N = 180 - 4x + 15

∠N = 195 - 4x

substitute x = 17°:

∠N = 195 - 4(17)

∠N = 127°