If one of the interior angles of a pentagon has a measure of 48 degrees, what is the average measure of the pentagon's other interior angles ?
sum of interior angles of a pentagon = 180(5-2) = 540
one is 48, so the remaining 4 have a sum of 492
average of remaining 4 angles = 492/4 = 123°
To find the average measure of the pentagon's other interior angles, we need to first determine the total measure of all the interior angles of a pentagon. The formula to find the sum of the interior angles of a polygon is (n - 2) * 180, where n is the number of sides.
In the case of a pentagon, n = 5, so the sum of the interior angles is (5 - 2) * 180 = 3 * 180 = 540 degrees.
Since one of the interior angles is given as 48 degrees, we need to find the sum of the other four interior angles. This can be done by subtracting the angle measure from the total sum: 540 - 48 = 492 degrees.
To find the average measure, we divide the sum of the other interior angles by the number of angles. In this case, we have 4 angles remaining, so the average measure is 492 / 4 = 123 degrees.
Therefore, the average measure of the pentagon's other interior angles is 123 degrees.