Geometry help?

Question

how do you find the number of sides of the regular polygon having given measure for the interior angle of 60

Answer 1

If the interior angles made by two straight lines w.r.t a third straight line is less than 90 degree, they should intersect and hence form a triangle. Since the total angles of a triangle is always equal to 180 degree and two angles are already known to be 60 degree the interior angle formed by the intersecting lines is 180 - (60 + 60) = 60 degree. Thus the polygon ia an equilateral triangle.

Answer 2

Use can use the Interior Angle Sum Theorum.

S=180(n-2)

S is the sum of the measures of the interior angles
n is the number of sides

Or you could use the Exterior Angle Sum Theorum
360/n =exterior angle
n= the number of sides

So, if you were to use 150 as the interior angle, to find the exterior angle take the supplement. (180-150=30)
Plug & chug. ^_^
360/n=30
360=30n
360/30=n
12=n

So the number of sides is twelve. Try it out using 60, you should get 3, an equilateral triangle.

Answer 3

Another method to find the the number of sides is
n=360/(180-interior angle) ; whence n stands for the number of sides.
Here, n=360/(180-60)= 3

Answer 4

the total number of degrees in the internal angles of a polygon of degree n is: 180(n-2)
total number of degrees in a regular polygon is: n*d where d is the # of degrees of 1 angle
60n=180(n-2)=180n-360
120n=360
n=3
equilateral triangle

Answer 5

There are 360 degrees in every polygon.

dividing by 60, there are six equal angles, meaning six equal sides, meaning hexagon.

Answer 6

if there are n sides then total angle = (n-2) * 180
now each angle is 60
so total angle = 60n = 180n - 360
or 120n = 360
n = 3
so it is a triangle

Answer 7

algebra 2 is better

Answer 8

i think its an equaliteral triangle