I need help with geometry!

Question

I need help! The measure of the seven angles in a nonagon measure 138 (degrees), 154 (degrees), 145 (degrees), 132 (degrees), 128 (degrees), 147 (degrees), and 130 (degrees). If the two remaining angles are equal in measure, what is the measure of each angle?

Answer 1

The equation for the sum of the angles in a polygon of "n" sides is (n - 2)180 so, since a nonagon has 9 sides, the sum of the angles is (9 - 2)180 = 7*180 = 1260°. Since 7 angles are known, we can add them all up and subtract it from 1260 to know the amount left for the 2 angles.

138 + 154 + 145 + 132 + 128 + 147 + 130 = 974

1260 - 974 = 286°

Since the two remaining angles are equal, we can just divide this number by 2 to get the measure of each angle. If you want to do it more "mathematically, you could let the measure of one of the unknown angles be "x". The other remaining angles is also "x" since they are equal. So:

x + x = 286

2x = 286 (then divide both sides by 2 to get:

x = 286/2

x = 143

Each remaining angle is 143°