The sum of the measures of the interior angles in a polygon is 540 degrees. How many sides does the polygon have?
To find the number of sides in a polygon with a given sum of interior angles, you can use the formula:
Sum of interior angles = (n - 2) * 180 degrees
where n is the number of sides in the polygon.
Given that the sum of the interior angles is 540 degrees, we can substitute this value into the formula:
540 = (n - 2) * 180
Next, we can simplify the equation:
540 = 180n - 360
To isolate the variable, we add 360 to both sides:
900 = 180n
Finally, we divide both sides by 180 to solve for n:
n = 900 / 180
n = 5
Therefore, the polygon has 5 sides.
To find the number of sides of a polygon given the sum of the measures of its interior angles, you can use the formula:
Number of sides = (Sum of interior angles) / (Interior angle of a polygon)
In this case, the sum of the measures of the interior angles is given as 540 degrees. Now, to find the interior angle of a polygon, you can use the formula:
Interior angle of a polygon = (180 * (n - 2)) / n
where 'n' represents the number of sides of the polygon.
Let's substitute the given values into the formula to find the number of sides:
Interior angle of a polygon = (180 * (n - 2)) / n
540 = (180 * (n - 2)) / n
Now, you can cross multiply to solve for 'n':
540n = 180 * (n - 2)
540n = 180n - 360
Subtract 180n from both sides:
540n - 180n = -360
Combine like terms:
360n = -360
Divide by 360:
n = -360 / 360
n = -1
Uh-oh! It seems like we have a negative number of sides, which is impossible for a polygon. This suggests there might be an error in the given information or the question itself. Please double-check the information provided or rephrase the question if necessary.
Remember that you're using (n-2)180 = 540.
Find n. :) It's after dividing by 180 and adding 2.