What is the measure of an exterior angle of a regular polygon in which the sum of interior angle measures is 5400 degrees?
A. 11.25 degrees
B. 30 degrees
C. 32 degrees
D. 168.75 degrees
Where’s the work?
A polygon with 5400 degrees interior angles has 32 sides.
360 / 32 = ?
To find the measure of an exterior angle of a regular polygon, we can use the formula:
Exterior angle = 360 degrees / number of sides of the polygon
In this case, we do not know the number of sides of the polygon, but we are given that the sum of the interior angle measures is 5400 degrees.
To find the number of sides of the polygon, we can use the formula:
Sum of interior angles = (number of sides - 2) * 180 degrees
By plugging in the given sum of 5400 degrees, we can solve for the number of sides:
5400 = (number of sides - 2) * 180
Dividing both sides by 180:
30 = number of sides - 2
Adding 2 to both sides:
number of sides = 32
Now that we know the number of sides is 32, we can use the formula for the measure of an exterior angle to find the answer:
Exterior angle = 360 degrees / 32
Calculating:
Exterior angle = 11.25 degrees
Therefore, the measure of an exterior angle of the given regular polygon is 11.25 degrees. So, the correct answer is A.