Question

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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°