Problem:

Can a parallelogram have two 45 ۫ and two 75 ۫ angles?

Why or why not?

Answer:

No. 

A parallelogram has two pairs of equal angles which are opposite to each other. 

However, a parallelogram is a quadrilateral and the interior angles of a quadrilateral have a sum of 360 ۫.

The given angles have a sum of 240 ۫ and so a parallelogram could not have the angles given.