Geometry Question? Please Answer asap thanks!?

Question

I do not understand how to do this problem? Please explain when giving an answer so I can understand this! Thanks!
The measure of an interior angle of a regular polygon is 120. Find the number of sides.

Answer 1

Wow. i'm a junior in nuclear engineering yet I don't know this? A regular polygon has all the sides the same length, as well as the angles right?

If so then 360/120 = 3. So it would be a triangle.

If the interior is from the inside of the polygon? Its been a while since Geometry in high school.

Answer 2

Here's how you would solve this problem in a general sense.

A regular polygon is one that has all sides and angles equal. It also means it's one that can be inscribed in a circle.

Picture an n-gon inscribed in the circle. If you draw all the radii from the center of the circle to the vertices, you will get n triangles (formed by 2 radii of adjacent vertices and the edge formed by those 2 vertices).

All the triangles will be isosceles and congruent. Let's call the angle measurements a, b, and b. The angle with measurement a is the one at the center of the circle. The measurement of the interior angle will be 2*b.

n*a = 360 (because all the triangles "add up" to a circle)
a+2b = 180 (triangle)
a = 180-2b
n*(180-2b) = 360
n = 360/(180-2b)

In this case, 2b = 120.

n = 360/(180-120) = 360/60 = 6

Answer 3

If the interior angle = 120, then an exterior angle = 180-120 = 60 degrees. Number of sides = 360/exterior angle
= 360/60 = 6.

Answer 4

the measure of an interior angle of a regular n-gon is

(n-2) × 180° / n = interior angle

6 sides

Answer 5

commence via arising equations from the suggestion this is given plus what you comprehend. all of us comprehend that the sum of the angles of a triangle = a hundred and eighty (or, a minimum of, we could continually comprehend this) all of us comprehend in an isosceles triangle, via definition, the backside angles are equivalent. enable us to assert that: V = the vertical perspective B = the backside perspective all of us comprehend that: B + B + V = a hundred and eighty a million) 2B + V = a hundred and eighty and a pair of) B = 2V exchange for B in equation a million 2(2V) + V = a hundred and eighty 4V + V = a hundred and eighty 5V = a hundred and eighty V =36 exchange V into equation 2 B = 2V B = 2(36) B = seventy two now plug interior the values for B and V into our unique equations to verify that we made no mistake a million) 2B + V = a hundred and eighty 2*seventy two + 36 = a hundred and eighty a hundred and forty four + 36 = a hundred and eighty a hundred and eighty = a hundred and eighty ......... exams out 2) B = 2V seventy two = 2*36 seventy two = seventy two ........ exams out For the 2d situation, only repeat the technique above to be certain in case you get B = 36 V = 108

Answer 6

i think the side side is 60..i guess.