one angle of an isosceles triangle is 40 degrees. what are the two possible sizes for the larger angle(s) in this triangle?

To find the two possible sizes for the larger angles in an isosceles triangle, we first need to determine the size of the other equal angle.

In an isosceles triangle, two angles are congruent (equal), and the third angle, called the base angle, is usually different.

Since one of the angles in the given triangle is 40 degrees, we can deduce that the other base angle is also 40 degrees because of the congruency of the triangle.

To find the size of the larger angle(s), we need to subtract the sum of the congruent angles from 180 degrees (the sum of the interior angles of a triangle).

So, larger angle = 180 degrees - (40 degrees + 40 degrees)

Simplifying, we get:

Larger angle = 180 degrees - 80 degrees

Larger angle = 100 degrees

Therefore, there is only one possible size for the larger angle in this triangle, which is 100 degrees.