A nonregular hexagon has five exterior angle measures of 55,58,69,57,and 55. What is the measure of the interior angle adjacent to the sixth exterior angle?

To find the measure of the interior angle adjacent to the sixth exterior angle, we need to find the sum of the exterior angles of a polygon.

The sum of the exterior angles of any polygon is always 360 degrees.

We are given five exterior angle measures: 55, 58, 69, 57, and 55 degrees.

To find the sixth exterior angle measure, we subtract the sum of the five known exterior angles from 360 degrees:

360 - (55 + 58 + 69 + 57 + 55) = 66 degrees

The answer is 66 degrees.

To find the measure of the interior angle adjacent to the sixth exterior angle, we can make use of the fact that the sum of the exterior angles of any polygon always equals 360 degrees.

In this case, we know the measures of five of the exterior angles: 55, 58, 69, 57, and 55. To find the measure of the sixth exterior angle, we can subtract the sum of the known exterior angles from 360:

360 - (55 + 58 + 69 + 57 + 55) = 360 - 294 = 66.

Therefore, the measure of the sixth exterior angle is 66 degrees.

Since the sum of an interior angle and its adjacent exterior angle is always 180 degrees for any polygon, we can find the measure of the interior angle adjacent to the sixth exterior angle:

180 - 66 = 114.

Hence, the measure of the interior angle adjacent to the sixth exterior angle is 114 degrees.

interior + exterior = 180º

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