If angles QNM, QNP, and MNP are right angles, find the length of NQ.

This is a flat pattern of the part from the original diagram.

Red dotted lines are bend lines.

NQ = NP = sin30º * 120            NQ = 60

Since  QNP  is a right angle   and angle QPN  = 45  then angle PQN  = 45

Then y = h

And since  QNM is a right angle then triangle QMN  is a  30-60-90 right triangle

Then x = sqrt (3)  h

And MNP is a right triangle with   angle MNP  =90...so....

Using the Pythagorean Theorem

120^2  =  x^2 + y^2

120^2  =  3h^2  + h^2

120^2 =  4h^2          take the square root of each side

120  = 2h

h  = 60   = QN