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?

Question

2734 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-01-06T22:59:20

#126˚#

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#,

#6x+144=900#

#6x=756#

#x=126#

The other six angles are #126˚#.