SOLUTION: ratio of number of sides of 2 regular polygon is 5:6. & ratio of there each interior angle is 24:25.find the number of sides of each polygon?

Click here to see ALL problems on Polygons

Question 669167: ratio of number of sides of 2 regular polygon is 5:6. & ratio of there each interior angle is 24:25.find the number of sides of each polygon?
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
your solution is that:
n1 = 10
n2 = 12
a1 = 144
a2 = 150

n = number of sides.
a = measure of the interior angle.
1 is for polygon number 1
2 is for polygon number 2

there's a lot of arithmetic involved, but the basics of the solution is as follows:

you have

you have

the formula for a1 is

the formula for a2 is

since the ratio of , you can substitute for a1 and a2 in that ratio to get:

you can cross multiply to get:

you have 1 equation in 2 unknowns.
you can reduce the number of unknowns by taking the ratio of n1 to n2 and solving for n2.

the ratio of n1 to n2 is given as

from that, you can solve for n2 to get

you now substitute for n2 in the equation of and solve for n1.

once you find n1, you can then find n2 and you can then find a1 and a2.

the math is tricky but the process works and i was able to find n1 = 10 and n2 = 12.

from that i was able to get a1 = 144 and a2 = 150.

the ratios hold up so the solution is good.