Question

abcdef is a regular hexagon.what is value of the exterior angle x ?

Answer 1

Answer:

The interior angle of a regular polygon can be found using the equation:

d = 180(n-2) / n

‘d’ is your interior degree and ’n’ is the number of sides your polygon has.

In your case, ’n’ is equal to 6.

d = 180(6–2) / 6 = 180(4) / 6 = 720 / 6 = 120

To find the exterior angle, simply subtract the interior degree from 180.

external degree = 180 - 120 = 60

The exterior angle of a regular hexagon is 60 degrees.

Answer 2

Answer:

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°