The floor of a gazebo is in the shape of a heptagon. Four of the interior angles measure 135∘. The other interior angles have eq

Question

Bogdan [553]

4 years ago

10

The floor of a gazebo is in the shape of a heptagon. Four of the interior angles measure 135∘. The other interior angles have eq

ual measures. Find their measures.

Mathematics

1 answer:

Lynna [10] · Answer 1 · 2021-11-15T12:52:50+03:00

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°