Question

With ∥MN ∥ QP and MQ

⊥ QP​
,MNPQ is a right trapezoid. Find
a) m∠m∠P, if m∠−m∠=31∘
m∠MNP−m∠M=31 ∘
b) the length of ‾NR, if =6 MN=6 in., =5 NP=5 in., and =9inQP=9in.

Answer 1

In a right trapezoid, we can find an angle and the length of a segment using given information.

Step-by-step explanation:

The given problem states that ∥MN ∥ QP and MQ ⊥ QP. Given these conditions, we can conclude that MNPQ is a right trapezoid.

For part (a), we are asked to find m∠P. Since m∠MNP - m∠M = 31°, we can determine that m∠P = m∠MNP - 31°.

For part (b), we need to find the length of NR. Using the given information that MN = 6 in., NP = 5 in., and QP = 9 in., we can apply the Pythagorean theorem to find the length of NR.