SOLUTION: in a regualr pentagon ABCDE draw diagonal BE and then find the measure of angle BAE,ABE and BED

The sum of the interior angles of a polygon is given
by the this formula, with N=5

(N-2)×180° = (5-2)×180° = 3×180° = 540°

And since all 5 interior angles of a regular polygon
have equal measure, each interior angle is  = 108°

Angle A is an interior angle so the measure of angle A is 108².

Triangle ABE is isosceles, its base angles have sum 180°-108° = 72°
Each base angle is half that, so angle ABE has measure 36°.

Angle AED is an interior angle of the regular pentagon, so
it has measure 108°.  Angle AEB is the other base angle of the
isosceles triangle ABE, so it is 36°.

Angle BED = Angle AED - Angle AEB = 108°-36° = 72°  

Edwin