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3 November, 05:02

The measures of angles of a hexagon 4x, 5x, 6x, 7x, 8x, 9x. calculate the size of the largest angle.

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  1. 3 November, 05:18
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    166 2/13 deg

    Step-by-step explanation:

    The sum of the measures of the interior angles of a convex polygon of n sides is 180 (n - 2).

    A hexagon has 6 sides, so n = 6.

    sum of measures of angles = 180 (n - 2) = 180 (6 - 2) = 180 (4) = 720

    4x + 5x + 6x + 7x + 8x + 9x = 720

    39x = 720

    x = 720/39

    x = 240/13

    The largest angle has measure 9x.

    9x = 9 * 240/13 = 2160/13

    2160/13 = 166 2/13

    Answer: 166 2/13 deg
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