SOLUTION: The measure of an interior angle of a regular polygon is given. Find the number of sides in each polygon 1.) 120 2.)150 I am at a complete lost here, could someone help me

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the interior and exterior angles are supplementary (they add to 180°)

the sum of the exterior angles of a polygon is 360°

1.) 180-120=60 ___ 360/60=6 ___ hexagon

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Remember:
there are two methods to find the measure of the angles of a regular , and for both of them we will use the fact that the
of the measures of the of a is degrees
could be divided

first method:

divide polygons into triangles by connecting one vertex to all of the others
you will see the :
if a polygon has , we would be able to make
if a polygon has , we would be able to make
if a polygon has , we would be able to make
:
: and so on

if we have a polygon with sides, we would be able to make triangles
So, in general, the measure of an interior angle of a regular is:



second method:

this method will be very similar to that of the first method;
the difference is that we will draw our triangles using one
point drawn the polygon
let start with the square:
the square could be divided into triangles; that means, the sum of all angles is
degrees
however, we need to take off the sum of the angles around that middle point which is degrees;
are involved with the angles of the square

so, we will have:
degrees
If we divide this sum of interior angles by the number of sides (or angles) in a square, we will get:
degrees………..it is a measure of each interior angle in a square

You can do same for other polygon.

In general, the measure of an of a regular is:


So, the number of sides in each polygon will be:

1.)
if the measure of is degrees, then the number of sides will be:






.............the number of sides

2.)
if the measure of is degrees, then the number of sides will be:






.................the number of sides