In rectangle MNPQ, m∠QMP = 2m∠NMP and MP = 12 ft. Find MQ.

Question

What is the length of MQ?

Answer 1

Sketch the rectangle with diagonal MP.

∠QMP and ∠NMP are complementary.  (They are parts of one of the corner angles.)

∠QMP is 2/3 of the right angle (60 deg) and  ∠NMP is 1/3 (30 deg).

The leg opposite the 30 deg angle in a right triangle is half the length of the hypotenuse.

That is MQ = 12/2 = 6.