Question

A quadrilateral has two angles of 110º and its diagonals bisect each other.
Which types of quadrilateral could it be?

Answer 1

If the two remaining angles are congruënt and opposite to each other, you have a rhombus;

If the two remaining angles are NOT congruënt but are opposite to each other, you have a "kite" (this may have another name);

If the two remaining angles are congruënt and adjacent to each other, you have a trapezium (US "trapezoid");

If the two remaining angles are NEITHER congruënt NOR opposite to each other, you have an irregular, but convex, quadrilateral.

DISCLAIMER: Being from the USA, I may have different names for geometric figures then are used elsewhere.