Question

Which quadrilateral has no right angle

Answer 1

The only one with two obtuse and two right angles.

Trapezoid

Answer 2

Squares and rectangles must all have exactly four right angles.

However,  quadrilateral that don't have to have four right angles are trapezoids, parallelograms and rhombi. 

trapezoids - different angles
parallelograms - 2 acute, 2 obtuse angles
rhombi - 2 acute, 2 obtuse angles

Note that a rhombus is a type of parallelogram.

Hope this helps! :)