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5 May, 16:07

A convex hexagon has interior angles with measures x^0, (5x - 103); (2x + 60), (7x - 31), (6x - 6), and (9x - 100), what is the value of x?

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  1. 5 May, 19:32
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    x = 30.66°

    Step-by-step explanation:

    The sum of the interior angles of a hexagon is 720°

    Each angles are x^0, (5x - 103); (2x + 60), (7x - 31), (6x - 6), and (9x - 100),

    we add all these angles together

    x^0 + (5x - 103) + (2x + 60) + (7x - 31) + (6x - 6) + (9x - 100) = 720

    x^0 = 1

    1 + (5x - 103) + (2x + 60) + (7x - 31) + (6x - 6) + (9x - 100)

    1 + 5x - 103 + 2x + 60 + 7x - 31 + 6x - 6 + 9x - 100 = 720

    1 - 103 + 60 - 31 - 6 - 100 + 5x + 2x + 7x + 6x + 9x = 720

    1 - 180 + 29x = 720

    -179 + 29x = 720

    29x = 720 + 179 = 889

    x = 889/29 = 30.655 ≅ 30.66°
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