Question 320446: If ABCDEF is a regular hexagon, how to calculate
Answer by CharlesG2(834)   (Show Source):
You can put this solution on YOUR website! If ABCDEF is a regular hexagon, how to calculate
(asking how to calculate angle ACD)...
the vertex of angle ACD is point C, rays CA and CD have a common endpoint at C,
now I think figuring out angle ACD depends on how you are labeling the vertices of the regular hexagon,
the interior angle of a regular polygon is (180(n-2))/n where n is number of sides,
3 sides --> (180(3-2))/3 = 180/3 = 60
4 sides --> (180(4-2))/4 = 360/4 = 90
5 sides --> (180(5-2))/5 = (180*3)/5 = 540/5 = 108
6 sides --> (180(6-2))/6 = 720/6 = 120,
I am labeling the vertices from top left and going clockwise ABCDEF,
angles ABC, BCD, CDE, DEF, EFA, and FAB are all 120 degrees,
in triangle ABC the angles should be 120-30-30, so angle ACB is 30 degrees,
then angle ACD = angle BCD - angle ACB = 108 - 30 = 78 degrees
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OKAY was informed that angle ACD should be 90 degrees and not 78 degrees.
Reading through my answer I gave now, oh dear I see what I did wrong...
Angle BCD is 120 degrees not 108 degrees.
And angle ACB is still 30 degrees.
So 120 - 30 = 90, and angle ACD is 90 degrees.
I apologize for any inconvenience I may have caused.
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