OpenStudy (anonymous):

exterior and interior angles of a nonagon?

2 years ago
OpenStudy (anonymous):

sum of the interior angles (i think) is \((n-2)\times 180\) so \[7\times 180=1260\] divide that by 9 to get the measure of each angle

2 years ago
OpenStudy (anonymous):

is that for the interior or exterior ?

2 years ago
OpenStudy (anonymous):

Interior angle - 140° Like any regular polygon, to find the interior angle we use the formula (180n–360)/n . For a nonagon, n=9.

2 years ago
OpenStudy (anonymous):

what about the exterior ?

2 years ago
OpenStudy (anonymous):

40° If you put a point in the middle of a nonagon and draw lines to each corner then you end up with 9 isoceles triangles where the angle in the center is 360 / 9 = 40 deg. That means the other two angles add up to (180 - 40) = 140 deg. That means each of the other angles in the triangle are 70 deg. Since the corner of the nonagon is the sum of the angles of the two triangles that make up the corner, the interior angle of a nonagon is 140 deg. Therefore the exterior angle of a nonagon is (180 - 140) = 40 deg.

2 years ago
OpenStudy (anonymous):

Thank you!!

2 years ago
OpenStudy (anonymous):

You're welcome. (:

2 years ago