Answer:
Each base angle is 80° and vertex angle is 20°.
Step-by-step explanation:
The triangle is shown for the given scenario.
From the isosceles triangle ABC, sides AB and AC are equal. So, angle B is equal to angle C.
Let the base angles be equal to [tex]x[/tex].
Therefore, the exterior angle of the base and the base angle form a linear pair and thus are supplementary angles.
For two angles to be supplementary, their sum is 180 degrees.
Therefore,
[tex]\angle ABE+\angle ABC=180\\100+x=180\\x=180-100=80[/tex]
So, each of the base angle is 80°.
Now, for a triangle ABC, the exterior angle is equal to the sum of the opposite interior angles. Therefore,
[tex]\angle ABE=\angle C+\angle A\\100=80+\angle A\\\angle A=100-80=20[/tex]
Therefore, the angle at the vertex is 20°.
