A picture frame is shaped as a heptagon. The measure of one angle is 126°. The remaining interior angles are congruent. What is the measure of each remaining interior angle in the picture frame?

180°

150°

129°

171°

Question

A picture frame is shaped as a heptagon. The measure of one angle is 126°. The remaining interior angles are congruent. What is the measure of each remaining interior angle in the picture frame?

 180°

 150°

 129°

 171°

anonymous · Answer

The sum of the measure of the interior angles of any figure is given by the formula
(n−2)180
where n is the number of sides. In this case, the sum of the interior angles of a heptagon is 900. The measure of one angle is 126, subtracting the remainder angles must ad to 774. Since they're congruent, they must all be of equal measure. Dividing by six, each angle must be 129.