A regular polygon has interior angles of 120 degrees. How many siddes does the polygon have?
interior angle = 120
so exterior angle = 180-120 = 60
all the way around is 360
360/60 = 6 or hexagon
To determine the number of sides of a regular polygon with interior angles of 120 degrees, we can use the formula for the sum of interior angles in a polygon.
The formula for the sum of interior angles in a polygon is given by:
Sum of interior angles = (n - 2) × 180 degrees
where 'n' represents the number of sides of the polygon.
Let's plug in the given information:
120 degrees = (n - 2) × 180 degrees
To solve for 'n', we can rearrange the equation:
120 degrees / 180 degrees = n - 2
Dividing both sides by 180 degrees:
0.67 = n - 2
Now, we can isolate 'n' by adding 2 to both sides:
0.67 + 2 = n
n ≈ 2.67
Since a polygon must have a whole number of sides, we round n to the nearest whole number to get the answer:
The polygon has approximately 3 sides.
Therefore, the regular polygon with interior angles of 120 degrees has 3 sides.