PLEASE HELP!!!! How many sides would there be in a convex polygon if the sum of all but one of its interior angles is 1070 degrees?

Question

PLEASE HELP!!!!
How many sides would there be in a convex polygon if the sum of all but one of its interior angles is 1070 degrees?

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Peyton 3 weeks 2021-09-26T19:41:13+00:00 2 Answers 0

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    0
    2021-09-26T19:42:38+00:00

    Try using 1070 degrees as the sum of the interior angles of a convex polygon, we get:

    1070 =[n – 2] x 180 (n = number of sides)
    1070 =180n – 360
    180n =1070+360
    180n =1430
    n = 1430 / 180
    n = 7.94 number of sides.

    Round the number up to 8 since 7.94 isn’t whole.

    So, the convex polygon is an octagon with sum of its interior angles:

    [8 – 2] x 180 =1080 degrees.

    0
    2021-09-26T19:43:02+00:00

    Answer:

    8

    Step-by-step explanation:

    The sum of the interior angles in any n-sided polygon is 180(n-2) degrees, so the angle measures in a polygon with 7 sides sum to 180(7-2) = 900 degrees, which means that the desired polygon has more than 7 sides. Meanwhile, the angle measures in a polygon with 8 sides sum to 180(8-2) = 1080 degrees. So, it’s possible that the polygon has 8 sides, and that the last angle measures 10 degrees

    To see that this is the only possibility, note that the angle measures in a polygon with 9 sides sum to 180(9-2) = 1260 degrees. Therefore, if the polygon has more than 8 sides, then the last interior angle must measure at least 1260 – 1070 = 190 degrees. But this is impossible because each interior angle of a convex polygon has measure less than 180.

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