Each triangle has three exterior angle measures (not necessarily distinct). Find all possible values of the sum of these measures in degrees. If you find multiple values, then list your answers in increasing order, separated by commas.

Never mind. Problem solved. All exterior angles of a triangle equal 360; Thanks, anyways,

The sum of the exterior angles of any polygon is always 360 degrees. Since a triangle is a polygon with three sides, it will have three exterior angles.

So, the sum of the measures of the exterior angles of a triangle is always 360 degrees. Therefore, there is only one possible value for the sum of the measures of the exterior angles of a triangle, which is 360 degrees.

To find the sum of exterior angle measures of a triangle, we need to consider the fact that the sum of the measures of exterior angles of any polygon is always 360 degrees.

In a triangle, we have three exterior angles. Let's assume these angles are \(a\), \(b\), and \(c\). Since the sum of the exterior angles of a triangle must be 360 degrees, we can write the equation:

\(a + b + c = 360\)

Now, we can analyze the possible values for \(a\), \(b\), and \(c\).

First, let's consider the largest possible value for one of the exterior angles. The largest possible exterior angle of any triangle is 180 degrees since an exterior angle cannot be greater than the straight angle, which measures 180 degrees.

Let's assume, without loss of generality, that \(a\) is the largest exterior angle, measuring 180 degrees:

\(a = 180\)

Now, we substitute this value into our equation:

\(180 + b + c = 360\)

By rearranging the terms, we find:

\(b + c = 360 - 180 = 180\)

So, the sum of the remaining two exterior angles (\(b + c\)) must be 180 degrees.

To find the minimum possible value for the sum of exterior angles, we need to consider the smallest possible value for one of the exterior angles. The smallest possible exterior angle of any triangle is 0 degrees since an exterior angle cannot be negative or less than 0.

Let's assume, without loss of generality, that \(a\) is the smallest exterior angle, measuring 0 degrees:

\(a = 0\)

Now, we substitute this value into our equation:

\(0 + b + c = 360\)

By rearranging the terms, we find:

\(b + c = 360 - 0 = 360\)

So, the sum of the remaining two exterior angles (\(b + c\)) must be 360 degrees.

Therefore, the possible values for the sum of the exterior angle measures in a triangle are 180 and 360 degrees. These are the only possible values, so the answer is:

180, 360