Question

I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT. Find the measure of one interior angle in the regular polygon.

Answer 1

`60 \textdegree`

Skills needed: Geometry

Explanation:

1) We are given a regular triangle.

A regular triangle is the same as an equilateral triangle. This means that:

--> All sides are of equal length (congruent)

--> All angles are of same measure (congruent)

-------------------------------------------------------------------------------------------------------------Another thing to remember is that the sum of all angles in a triangle is 180 DEGREES.

------------------------------------------------------------------------------------------------------------- 2) Let's make an equation:

Let's make one of the angles a variable:
`y`

ALL the angles of the triangle will have a measure of "
`y`", which means that each of the angles equals
`y`.

---> Sum of all angles (IN VARIABLE TERMS):
`y+y+y=3y` (1y+1y+1y = 3y)

ALSO:

- Sum of all angles is 180. This can be the right side of the equation.

`3y = 180` is our equation based on all the information above.

We want to then isolate
, so we have to divide by 3.

`3y / 3=180 / 3`

`3y / 3=y, 180 / 3 = 60` (doing both division problems)

This means that:
`y=60`

60 should be the answer.

Answer 2

60 degrees
Total is 180
So 180/3=60