The formula for calculating the TOTAL of the interior angles of an n-sided polygon is:
Angle Sum = 180 (n-2) degrees
So for a regular polygon, each of the identical interior angles will be 180(n-2)/n
The equivalent formula is 180 - (360/n), where 360/n is a single exterior angle, supplementary.
How many sides does a regular polygon have if the measure of each interior angle is equal to 172 degress ?
A 16 sided polygon.
A regular polygon has sides of equal length and each interior angle is the same measure
The polygon will have 12 equal sides and each interior angle measures 150 degrees.
Each interior angle of a regular polygon has a measure that is equal to one hundred and eighty degrees times two less than the number of sides in the polygon.
It will have 10 equal sides
For a regular polygon with sides n, the sum of the interior angles = (n-2)180Therefore, a regular polygon has interior angle sum equal to 540o.(5-2)180=(3)180=540
A regular hexagon which has 6 equal sides and 6 equal angles.
The equation for finding the interior angle measures of a regular n-gon is (n-2)*180/n. Thus, if this is set equal to 176 and solved for n, n is found to be 90. Therefore, a regular polygon with each interior angle measure equal to 176, has 90 sides.
6 sides and it is a regular hexagon
Five. It is a regular pentagon.
The interior angle is a regular polygon is equal to 180-360/n, where n is the number of sides. For a 17-sided regular polygon, 180-360/n is approximately 158.824 degrees.