The exterior angle of a regular polygon is one fifth of its interior angle. How many sides the polygon has?
Answers
Step-by-step explanation:
The exterior angle of a polygon is 1/5 of the interior angle. How many sides does a polygon have?
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the sum of the exterior angles of a polygon with n sides is always 360° - for any integer, n. so each of the n exterior angles individually would measure 360n °.
The sum of the interior angles of a polygon with n sides depends on the value of n, (the number of sides). The sum of interior angles is 180(n-2)°, so each interior angle is equal to 180(n−2)n °.
so in the question here, the given information says the following:
360n = 15⋅180(n−2)n
solve for n to find the number of sides.
cross multiply maybe….
180n(n-2) = (360)(5n)
(n-2) = (2)(5)
n-2 = 10
n= 12.
Polygon has 12 sides.