Find angles in trapezoid with sides' lengths equal $15$, $7$, $7$, $8$ 
What are the interior angles in the trapezoid with sides whose lengths equal  $15$, $7$, $7$, $8$ (sides with lengths $15$ and $7$ are parallel)?

I found this problem in elementary school's problem book. We should not use any trigonometry. Is there some simple solution, or the problem has some typo?

Draw perpendiculars from the upper base of length 7 to the lower base of length 15. 
You cannot possibly find the interior angles without trigonometry.
