We know that an exterior angle of an isosceles triangle has a measure of 100. Therefore, m ∠ 1 = 100 and we can find the measure of one of the angles in the triangle, ∠ 2.
100+ m ∠ 2 = 180 ⇔ m ∠ 2 = 80
Now, we know that one of the angles in an isosceles triangle has a measure of 80.
It can be either the measure of the vertex angle or the measure of one of the base angles. Let's find the possible sets of measures by considering these two options.
Vertex angle
We know that the measures of the base angles are the same, x. Also, we assume that the measure of the vertex angle is 80. Therefore, by the Triangle Angle-Sum Theorem we get the following equation.
2x+80=180 ⇔ x=50
We can tell that if the measure of the vertex angle is 80, then the measures of the base angles are 50 and 50.
Base angle
Now, we assume that the measure of one of the base angles is 80. Since base angles are congruent, we can conclude that the measure of the second base angle is also 80. Let's call the measure of the vertex angle y and find it with the Triangle Angle-Sum Theorem.
80+80+y=180 ⇔ y=20
We can tell that if the measure of one of the base angles is 80, then the measures of the other base angle is also 80, and the measure of the vertex angle is 20.
