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]:
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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
- -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.
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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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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