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°