Given that an isosceles triangle has an exterior angle of its base angle that is 130°, the two possible sets of angles obtainable in the triangle are:
- Base angles: [tex]\mathbf{30^{\circ}}[/tex]
- Vertex angle: [tex]\mathbf{80^{\circ}}[/tex]
Recall:
- An isosceles triangle has two equal base angles and two equal sides.
Thus:
The isosceles triangle has been given in the image attached below to show the possible angle measures we can get.
In figure 1, we see that when the exterior angle of the bases is 130°, the measure of each of the base angles would be:
[tex]\mathbf{180 - 130 = 50^{\circ}}[/tex]
The vertex angle would be:
[tex]\mathbf{180 - (50 + 50) = 80^{\circ}}[/tex]
Therefore, given that an isosceles triangle has an exterior angle of its base angle that is 130°, the two possible sets of angles obtainable in the triangle are:
- Base angles: [tex]\mathbf{30^{\circ}}[/tex]
- Vertex angle: [tex]\mathbf{80^{\circ}}[/tex]
Learn more here:
https://brainly.com/question/17475213
