SOLUTION: A polygon has n sides. Two of its angles are right angles and each of the remaining angles is 144 degrees. Find the value of n.

Algebra ->  Polygons -> SOLUTION: A polygon has n sides. Two of its angles are right angles and each of the remaining angles is 144 degrees. Find the value of n.      Log On


   

Question 760100: A polygon has n sides. Two of its angles are right angles and each of the remaining angles is 144 degrees. Find the value of n.
Found 2 solutions by DrBeeee, josgarithmetic:
Answer by DrBeeee(684) About Me  (Show Source):
You can put this solution on YOUR website!
Use the formula that states that the sum of the angles of an n-sided polygon is given by
(1) S = 180*(n - 2)
We know that the sum is
(2) S = 90 + 90 + (n - 2)*144 where the last expression represent the fact that the remaining non-right angles (n-2) are each 144 degrees.
Therefore setting (2) equal to (1) we get
(3) S = 90 + 90 + (n - 2)*144 = 180*(n - 2) or
(4) 180 = (n - 2)*(180 - 144) or
(5) 180 = 36*(n - 2) or
(6) n - 2 = 180/36 or
(7) n - 2 = 5 or
(8) n = 7
Answer: The polygon has seven sides.

Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
SIDES___________TOTAL DEGREES
3_______________180
4_______________180*2
5_______________180*3
6_______________180*4
n_______________180(n-2)

You case indicates %28180%28n-4%29%29%2F%28n-2%29=144.
You have 2*90 plus (n-4)*144 total degrees where n is also the count of the angles. The 144 degree angles will sum to 144%28n-2%29 degrees. You account for the triangles associated with these using 180%28n-4%29 degrees, because two OTHER angles are 90 degrees each.
15(n-4)=(n-2)12
5(n-4)=4(n-2)
5n-20=4n-8
n=20-8
n=12