In a regular polygon (equal sides and angles), you use (n-2)180 to find out what the interior angle sum is (n=number of sides in polygon) and you divide by that number by whatever n is to find out the measure of an individual angle, right? Well, there is going to be a problem on tomorrow's geometry test where we are given the measure of an interior angle of a regular polygon (for instance, one angle=150 degrees), but I can't tell how to do that. I figured it would be something like this:
(n-2)180
-------- = 150
n
But, it dosn't work out too well when I try to single out n. Can someone tell me how to do this?
P.S. Sorry that my explanation was so long -- I was trying to get the information out there :-) THANKS!!!
Take an interior angle: 150 degrees. How many sides?
the sum of interior angles is 150n (n angles, each 150 degrees)
but (n-2)180= 150n (both are sum of interior angles, and equal, so
180n-360=150n
30n=360
n= 12
\thats it.
Oh -- I get it! Thank you so much for helping me out, I really needed that info for tomorrow's test. Thx!
i have absolutely no idea how to do this!
No problem, let me help you with that!
To find the number of sides (n) of a regular polygon given the measure of an interior angle, you can rearrange the formula you mentioned.
Start by multiplying both sides of the equation by n to get rid of the division:
(n-2) * 180 = 150 * n
Now distribute the 180 on the left side:
180n - 360 = 150n
Next, move the terms containing n to one side of the equation by subtracting 150n from both sides:
180n - 150n = 360
Combine like terms:
30n = 360
Finally, divide both sides of the equation by 30 to solve for n:
n = 360 / 30 = 12
So, the regular polygon has 12 sides.
Remember, this process represents one way to solve the problem. You can always check your answer by substituting the value of n back into the original equation.