High School

Given that \( MN \parallel QP \) and \( MQ \perp QP \), \( MNPQ \) is a right trapezoid.

Find:

a) \( m\angle P \), if \( m\angle MNP - m\angle M = 31^\circ \).

b) The length of \( \overline{NR} \), if \( MN = 6 \) in., \( NP = 5 \) in., and \( QP = 9 \) in.

Answer :

Final answer:

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

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.

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