SOLUTION: what is the sum of the exterior angles of a 24-agon ? What is the measure of each interior angle of a regular heptagon? How many sides does a equiangular polygon have

Algebra ->  Polygons -> SOLUTION: what is the sum of the exterior angles of a 24-agon ? What is the measure of each interior angle of a regular heptagon? How many sides does a equiangular polygon have      Log On


   

Question 261732:
what is the sum of the exterior angles of a 24-agon ?

What is the measure of each interior angle of a regular heptagon?


How many sides does a equiangular polygon have if each interior angle is 144?
Answer by roseo(33) About Me  (Show Source):
You can put this solution on YOUR website!
The sum of the exterior angles for any polygon is 360 degrees.
Because a heptagon has 7 angles therefore each of the exterior angles is 360/7 therefore the interior angle is 180 - 360/7 or 129 4/7. The sum of an exterior angle and its corresponding interior angle is 180 degrees.
If the interior angle 144 degrees then the corresponding exterior angle is 36 degrees. Remember that the exterior angles must add up to 360 degrees so 360/36 is 10. There would be 10 sides to the polygon.