You are given the measure of each interior angle of a regular n-gon. Find the value of n.

1. 135
2. 156
3. 162
4. 172 4/5


Does n mean sides? Please help me. Thanks!

YES Erica, n is the number of sides.....

The other fellow shows you the book method. Here is a QUICK method

Look at number 1) 135 is the Interior Angle
The Exterior Angle is Supplementary to the Interior Angle.
To find the measure of the Exterior Angle Just Subtract......180 - 135 = 45
NOW DIVIDE (ALWAYS) 360 by 45............360 / 45 = 8 sides........n = 8

2).....180 - 156 = 24.............360 / 24 = 15 sides.........n = 15

3).....180 - 162 = 15.............360 / 15 = 24 sides........n = 24

4).....180 - 172.8 = 7.2.........360 / 7.2 = 50 sides........n = 50

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The sum of all interior angles of an n-gon ( figure with n regular sides) = n180 - 360 this is a

formula If you divide the sum of n angles by n you get each angle!! for example the sum of 5
interior angles angles of a pentagon = 5(180)- 360 sum = 540 to find each angle you divide by 5 and get 108 degrees
Case 1 sum of interior angles of an n-gon = n(180)-360 to find the particulat angle you divide by n

(180n-360)/n = 135 180n-360 = 135n 180n- 135n = 360 45n = 360 n = 8