A picture frame is shaped as a heptagon. The measure of one angle is 144°. The remaining interior angles are congruent. What is the measure of each remaining interior angle in the picture frame?

Jan 6, 2016

126˚

Explanation:

A heptagon has $7$ sides.

To find the total sum of the interior angles of a polygon with $n$ sides, use the formula

180˚(n-2)

Since $n = 7$, a heptagon's interior angles have a sum of

180˚(7-2)=900˚

We know that $1$ angle is 144˚ and that the other $6$ angles are congruent. Thus, if the measure of just one of the angles is $x$,

$6 x + 144 = 900$

$6 x = 756$

$x = 126$

The other six angles are 126˚.