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If the measure of each interior angle of a regular polygon is 171, what is the number of sides in the polygon?

2 Answers
Feb 18, 2016

Answer:

The polygon will have 40 sides.

Explanation:

The measure of the interior angles of a polygon is determined by the formula

#((n - 2)180)/n# = interior angle measure

were #n# is the number of angles and sides of the polygon.

We know that the interior angles of the polygon in the question have measures of #171^o#

#((n - 2)180)/n = 171^o#
#((n - 2)180) = 171^o(n)#
#180n - 360 = 171n#
# -360 = 171n-180n#
#-360 = -9n#
#-360/-9 = n#
#40 = n#

The polygon will have 40 sides.

May 17, 2018

Answer:

Use the exterior angle to find there are #40# sides

Explanation:

The interior angle and the exterior angle of a polygon are adjacent supplementary angles. This means that they add to #180°#

Each exterior angle #= 180°-171° = 9°#

The sum of the exterior angles of any polygon is #360°#

#"Number of sides" = (360°)/"exterior angle"#

#"Number of sides" = (360°)/(9°) = 40# .