SOLUTION: what do all the angles inside a heptagon add up to ?

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Question 73685: what do all the angles inside a heptagon add up to ?
Answer by jim_thompson5910(35256) About Me  (Show Source):
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Find the interior angle
Solved by pluggable solver: internal angle of polygon

Interior angle of a Regular Polygon

The interior angles of any Polygon always add up to a constant value, which depends only on the number of sides. For example the interior angles of a pentagon always add up to 540° no matter if it regular or irregular, convex or concave, or what size and shape it is. The sum of the interior angles of a polygon is given by the formula

Sum=180%2A%28n-2%29

where n is the number of sides

For a regular polygon, the total described above is spread evenly among all the interior angles, since they all have the same values.Hence all interior angles will be equal.

Therefore,
Each+Interior+Angle=%28%28180%2A%28n-2%29%29%2Fn%29

Each+Interior+Angle=%28180%2A%287-2%29%29%2F7=128.571428571429

Conversion of angles from degrees to radian:
The relation between two units of angle measurement is :

2*pi rad = 360 degrees

The Interior angle in Radians,

Each+Interior+Angle=%28%28%28180%2A%28n-2%29%29%2Fn%29%2A2%2Api%2F360%29

Each+Interior+Angle=%28%28180%2A%287-2%29%29%2F7%29%2A2%2Api%2F360=2.24399475

Hence, The interior angle of a Polygon is 128.571428571429 degrees and 2.24399475 radians.

For more on this topic, See the lessons on Geometry Area of Regular Polygon

Some more is on Geometry Special Quadrilaterals


Multiply this by 7 to find the sum of the 7 angles
7(128.57)=899.99 degrees
or
7(2.24)=15.68 radians