Question

abcdef is a regular hexagon. find each angle of abe

Answer 1

Draw regular hexagon ABCDEF with triangle ABE inside it.
All sides of hexagon are equal in length
Sum of angles of a polygon = (n - 2)180 
       n = number of sides
Sum of angles of a hexagon is 720°, since it is a regular 
hexagon each interior angle has measure 120°
Quadrilateral ABEF contains half the angle measure of the
hexagon; its interior angle measure = 360°
angle AFE = 120° (angle of hexagon ABCDEF)
triangle AFE is isosceles; angle FAE = angle FEA = 30°
           sum of angles of triangle = 180°
angle FAE + angle EAB = 120°; therefor angle EAB = 90°
angle ABE is one half of 120° = 60°
angle ABE + angle EAB + angle AEB = 180°
         therfor angle AEB = 30°