the measure of an interior angel of a regular polygon is 150. find the number of sides in the polygon.

The polygon has sides.

Step-by-step explanation:

Recall that the expression for finding the measure of one interior angle of a regular polygon is , where is the number of sides the polygon has (and ), which is what we want to find.

Because the measure of one interior angle of the given polygon is , we can write the following equation to solve for :

Solving for , we get:

(Distribute the in the numerator)

(Multiply both sides of the equation by to eliminate the denominator and simplify)

(Subtract from both sides of the equation and simplify)

(Add to both sides of the equation to isolate and simplify)

(Divide both sides of the equation by to get rid of 's coefficient and simplify)

Therefore, the polygon has sides. Hope this helps!

18

step-by-step explanation:

draw the shape and you will see that f and k are actually at adjacent vertices (points of the hexagon that are neighboring).   so find the distance between (1,2) and (4,2).   that is easy since (1,2) and (4,2) is just a vertical distance to count, which is 3.   it is a regular polygon which means all sides are congruent.   you have 6 sides (hexa) so multiply 6 by 3 to receive 18.

salary

step-by-step explanation: