A triangle has two congruent angles and an exterior angle with measure 100. Find two possible sets of measures for the angles of the triangle.

To find the measures of the angles in a triangle, we can make use of the fact that the sum of the angles in any triangle is always 180 degrees.

Let's assign variables to the measures of the angles. Let's denote the congruent angles as x and the measure of the exterior angle as y.

Since the triangle has two congruent angles, we have:
x + x + y = 180

Since the given exterior angle measures 100 degrees, we can set y as 100:
2x + 100 = 180

Now, we can solve this equation to find the value of x:
2x = 180 - 100
2x = 80
x = 80/2
x = 40

Now, we can substitute the value of x back into the equation to find y:
2(40) + 100 = 180
80 + 100 = 180
180 = 180

So, one possible set of measures for the angles of the triangle is: 40°, 40°, 100°.

Let's find another set of measures for the angles:

Since the triangle has two congruent angles, let's assume that each congruent angle measures x, and the exterior angle measures y.

We can set up the equation:
x + x + y = 180

From the given information, we know that the exterior angle measures 100 degrees, so we can write:
2x + 100 = 180

Solving this equation for x:
2x = 180 - 100
2x = 80
x = 40

Now, let's substitute the value of x back into the equation to find y:
2(40) + y = 180
80 + y = 180
y = 180 - 80
y = 100

Therefore, another possible set of measures for the angles of the triangle is: 40°, 40°, 100°.

To summarize, two possible sets of measures for the angles of the triangle are:
1) 40°, 40°, 100°
2) 40°, 40°, 100°