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?

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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˚#.