the measure of each interior angle of a regular polygon is 156 how many sides does the polygon have explain how you got your answer

Answer 1

Any closed even angle/side shape has 360° center.

Answer 2

15

formula for the sum of the interior angles of an "n" sided polygon = 180(n-2)

divide by n to get the average value of one interior angle: 180n-360 divided by n = 180-360/n

156 = 180- 360/n

360/n = 180-156 = 24

n =360/24 = 15 sides to the polygon

a triangle has 3 sides with interior angle = 60

quadrilateral has 4 sides with interior angle =90

the more sides the larger the interior angle

in the limit as sides approach infinity, the angle approaches 180 and the polygon becomes a circle

Answer 3

The sum of the interior angles of a polygon is 180 * (n-2), where n is the number of sides.

For a regular polygon, where all sides and interior angles are equal, each interior angle is equal to the above sum divided by the number of sides:

180 * (n-2) / n

We are given that each interior angle is 156, thus

156 = 180 * (n-2) /n

156 * n = 180 * (n-2)

156*n = 180n - 360

-24n = -360

n = 15

Answer 4

All angle measures are in degrees. The sum of the interior angles of a polygon with n sides is equal to 180*(n-2). [As a check, note that when the polygon is a triangle, n=3 and the formula gives us 180*(3-2)=180 which is what we expect, and when the polygon is a rectangle or parallelogram, n=4 and the formula gives us 180*(4-2)=360 which, again, i exactly what we expect.]

We are given that the interior angles of the problem's polygon is the number of angles multiplied by156. The number of interior angles, of course, is the same as the number of sides, so 156*n=180*(n-2). So n=15.and the polygon has 15 sides.

Let's check: 180*(15-2)=2340. 15*156=2340..