Polygons

Geometry Level 2

One interior angle of a regular polygon measures 179 degrees. How many sides does it have?


The answer is 360.

Nico Anthony Tejano by Nico Anthony Tejano , 33, Philippines

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2 solutions

Edwin Gray
Feb 25, 2019

The total number of degrees internal to a regular polygon of n sides is 189(n - 2), so each angle is 180(n - 2)/n. if this equals 179, then 180(n - 2 ) = 179n, or 180 n - 360 = 179n, and n = 360.

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Harshendu Mahto
Jan 18, 2016

Sum of interior angles of a regular polygon = 180(n-2) , where 'n' is number of sides.

Here, let the number of side be 'n'.

Therefore,

180(n-2) = 179 x Number of angles

=> 180(n-2) = 179n [Number of sides = Number of angles=n]

=> 180n - 360 = 179n

=> 180n - 179n = 360

=> n = 360

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