SOLUTION: Seven of the interior angles of a nonagon add up to 1020� and one of the remaining angles is twice the other. Find the size of each remaining angle

Question 990236: Seven of the interior angles of a nonagon add up to 1020� and one of the remaining angles is twice the other. Find the size of each remaining angle

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
one of the angles will be 80 degrees.
the other angle will be 160 degrees.
the sum of the angles of the nonagon will be equal to 1020 + 240 = 1260.

a nonagon has 9 sides.
the sum of the angles of the nonagon are equal to (9-2)*180 = 7 * 180 = 1260.
the sum of the angles of a nonagon is also equal to 9 * (180 - 360 / 9) which is equal to 9 * 140 which is equal to 1260.
both formulas lead to the same sum of angle of a nonagon (nine sided figure).
once you know that, it's a simple formula to derive the angles.
let one of the angle = x and the other angle = 2x.
their sum is 3x.
1020 + 3x = 1260
3x = 1260 - 1020
3x = 240
x = 80.
2x = 160.

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