4. If the measure of the exterior angles of a regular polygon is 60 degrees , how many sides does the polygon have?
5. The angle sum in a regular 5 -gon is _______.
B) 180 * 4
C) 180 * 3
D) None of the other choices
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a+b+c+d+e = 360
Recall: for a convex polygon, the sum of the exterior angles will always be 60. If a polygon is regular, all of its exterior angles will be equal. So,
m of ext angle in a reg polygon = 360/n where n is the number of sides. Transforming the equation, we can discover that:
number of sides/vertices/angles/whatever you wanna call it = 360/m of ea ext angle
= 360/60 = 6
THM: sum of int angles in a convex polygon with n sides is (n - 2)180
Plugging in our value of n which is 5, we get 3*180 = 180*3 so the answer is C.
would i use this formula? (n-2) × 180°
thank you, bluepig
The measure of an exterior angle in a regular 11-gon is _______.
The measure of a vertex angle in a regular 15 -gon is ________.
You know enough now to solve the first question. You know enough to figure out how to solve the second one, but you'll need to think a bit. I think it'll be more rewarding if you do it yourself and you're definitely capable of it.