Question 36

If $$ABCDEF$$ is a regular hexagon, then what is the value (in degrees) of $$\angle AEB$$?

Solution

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°

B is correct choice.

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