SOLUTION: An n-sided regular polygon has 5 more sides than an m-sided regular polygon, and the sum of interior angles of the former is twice the latter. Find n and m.

Algebra ->  Polygons -> SOLUTION: An n-sided regular polygon has 5 more sides than an m-sided regular polygon, and the sum of interior angles of the former is twice the latter. Find n and m.      Log On


   

Question 1006813: An n-sided regular polygon has 5 more sides than an m-sided regular polygon, and the sum of interior angles of the former is twice the latter. Find n and m.
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
One interior angle measure is 180%28x-2%29%2Fx for any regular x-gon. You can find that using your own investigation and identify the pattern. The sum of the interior angles of this x-gon will be 180%28x-2%29.

Analyzing your exercise description, n-gon is the "former" and m-gon is the "latter"; system%28n-m=5%2C180%28n-2%29=2%2A180%28m-2%29%29.

Simplifying the system should give something equivalent to system%282m-n=2%2Cn-m=5%29.


highlight%28system%28n=12%2Cm=7%29%29