Question

If DEFG is a kite, find the measure of angle EFG

Answer 1

Since kites have two distinct pairs of consecutive, congruent sides their diagonals are perpendicular and one diagonal
bisects the other.

Since perpendicular lines intersect at 90° every triangle in a kite is a right triangle. Since it is given that angle DEF is 72° and we know triangles equal 180°

72+90=162
180-162 =18

so angle EFD is 18° and because angle EFD is a bisected part of angle EFG - 18x2=36

so angle EFG is 36°