ABCDEF is a regular hexagon inscribed in a circle centre 0, radius 10cm. Calculate the angle DOE
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Answer:
60°
Step-by-step explanation:
As it is a regular hexagon, all six of the angles AOB, BOC, COD, DOE, EOF, FOA are equal. They add up to 360°, so each is 60°.
The radius being 10cm is a red herring.
Answered by
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°
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°
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