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.

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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