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.

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) (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(39617) (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 .
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 degrees. You account for the triangles associated with these using 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
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