SOLUTION: each interior of a regular polygon is 174 degrees what is each exterior angle?
how many sides does the polygon have?
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Question 238770: each interior of a regular polygon is 174 degrees what is each exterior angle?
how many sides does the polygon have?
Found 2 solutions by Earlsdon, JimboP1977:
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
The measure of each interior angle of a regular polygon of n sides can be expressed by:
In this problem, degrees, so we substitute...
Multiply both sides by n and simplify.
Add 360 to both sides.
Subtract 174n from both sides.
Finally, divide both sides by 6.
The polygon has 60 sides.
The exterior angle is supplement of the interior angle, so...
degrees.
Answer by JimboP1977(311) (Show Source): You can put this solution on YOUR website!
Well a triangle has interior angles totalling 180
a square has interior angles totalling 360
a pentagon (5 sided) has interior angles totalling 540
a hexagon (6 sided) has interior angles totalling 720
so in general a n sided shape has interior angles totalling (n-2)*180. If it is regular n sided shape then each interior angle = (180*(n-2))/n
174 = (180(n-2))/n
174n = 180n-360
174n-180n = -360
-6n=-360
n = 60
180 - 174 = 6 degrees which is the exterior angle
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