Regular polygons meet in life every day, for example, a square, a triangle or a hexagon in the form of which all bee cells are made. To construct a regular polygon independently, it is necessary to know its corners.
Instruction
1. At first = 180 ⁰ (n-2) calculate the sum of internal corners of your polygon by formula S. For example, if you need to find corners of a regular polygon with 15 parties, substitute n=15 in the equation. At you it will turn out S=180 ⁰ (15-2), S=180x13, S=2340 ⁰.
2. Further divide the received sum of internal corners into their quantity. For example, with a polygon the quantity of corners is equal in an example to the number of the parties, that is 15. Thus, you receive that the corner is equal 2340 ⁰/15=156 ⁰. Each internal corner of a polygon is equal 156 ⁰.
3. If it is more convenient to you to calculate polygon corners in radians, act as follows. Subtract number 2 from the number of the parties and increase the received difference by number P (Pi). Then divide the work into quantity of corners in a polygon. For example, if you need to calculate corners of the correct 15th square, act so: P * (15-2)/15=13/15P, either 0.87P, or 2.72 (but, as a rule, number P remains unchanged). Or just divide the corner size in degrees into 57.3 - so many degrees contain in one radian.
4. Also you can try to calculate corners of a regular polygon in grads. For this purpose subtract number 2 from the number of the parties, divide the received number into the number of the parties and increase result by 200. This unit of measure of corners is almost not used today, but if you decided to count corners in grads, do not forget that the hail breaks into metric seconds and minutes (for 100 seconds in a minute).
5. Perhaps, you need to calculate an external corner of a regular polygon, in this case act this way. Subtract from 180 ⁰ an internal corner – as a result you receive value of an adjacent, that is external corner. It can accept value from-180 ⁰ up to +180 ⁰.