How many sides does a polygon have if the sum of the interior angles is 2340

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Question 253091: If the sum of the interior angles of a polygon is 2340, how many sides does the polygon have?
Answer by MRperkins(300)   (Show Source):

You can put this solution on YOUR website!
FORMULA: (n-2)180=sum of the interior angles.
Where n=number of angles of a regular polygon.
We know that the sum of the interior angles is 2340
so
(n-2)180=2340 divide both sides by 180 and get
n-2=13 add 2 to both sides and get
n=15 Therefore, this polygon has 15 sides.
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Answer:

15 sides

1. -A regular polygon has 15 sides. Find the measure of each angle. All interior angle add up to(n-2) 180 degrees. therefore all the interior angle of your 15 sides regular polygon add up to 15-2=13180 degrees=2340 degrees.

If sum of all the interior angles of a polygon is #2340^@#, how many sides does it have?

Geometry Angles and Intersecting Lines Angles with Triangles and Polygons

1 Answer

Shwetank Mauria

Feb 24, 2017

#s=15#

Explanation:

Whatever the number of sides of a polygon,

the sum of its exterior angles is always#360^@#

Further, each pair of exterior angle and interior angle adds up to#180^@#

Hence in a polygon with#s#sides (or angles),

the sum of all the interior and exterior angles would be#180^@xxs#

and sum of interior angles would be#180^@xxn-360^@=180^@(s-2)#

As sum of angles is#2340^@#

Hence,#180(s-2)=2340#or#s-2=2340/180=13#

and#s=13+2=15#and polygon is a Pentadecagon.

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The sum of a polygon’s interior angle measures is 2340 degrees. What kind of polygon is it?

Geometry Angles and Intersecting Lines Angles with Triangles and Polygons

1 Answer

SagarStudy

Jan 3, 2016

We know that sum of interior angles of a#n#sided polygon is given by#(n-2)*180#degree.
Where#n#is the number of sides.

Here sum of interior angels is#2340#degrees.
#implies (n-2)*180=2340#
#implies n-2=13#
#implies n=15#
#implies#number of sides#=15#
Therefore, the polygon is 15 sided.

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