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10 June, 17:01

The floor of a gazebo is in the shape of a heptagon. Four of the interior angles measure 135∘. The other interior angles have equal measures. Find their measures.

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  1. 10 June, 17:58
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    The other interior angles are each 120°.

    We first find the sum of the measures of the interior angles of a heptagon. We use (n-2) (180) to find this:

    (7-2) (180) = 900

    We can now set up an equation. We know that 4 of the angles are 135° each, and we will let the unknown angle measure be x:

    4 (135) + 3x = 900

    540 + 3x = 900

    Subtract 540 from each side:

    540 + 3x - 540 = 900 - 540

    3x = 360

    Divide both sides by 3:

    3x/3 = 360/3

    x = 120°
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