An exterior angle of an isosceles triangle has measure of 100 degrees. if the exterior angle of the bases is 100 degrees then the measure of each angle base and vertex is

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 .

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,

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,

Therefore, the angle at the vertex is 20°.

answer: option a.

step-by-step explanation:

you know that the quadrilateral opqr ( a four sided figure) is inscribed in circle. this means that all its vertices are on the circle.

then, by definition, the opposite angles of the quadrilateral are supplementary, this means that the sum of their measures is 180 degrees.

you can observe in the figure that the angles ∠opq   and the angle ∠orq   are opposite, therefore:

then, can be used to d to calculate the measure of ∠opq