The degree measure of the angle between the sides of an isosceles triangle is 46 degrees.

The degree measure of the angle between the sides of an isosceles triangle is 46 degrees. Find the degree measure of the remaining angles if the sum of all the angles of the triangle is 180 degrees.

Using the theorem on the sum of all angles of a triangle, equal to 180 degrees, you can calculate the sum of two unknown angles at the base, by subtracting a known angle:

180 – 46 = 134 degrees

From the properties of an isosceles triangle, it follows that the angles at the base are equal, which means:

134/2 = 67 degrees is equal to both the second and third angles of the triangle.

Answer: the first angle is 46, the second angle is 67, the third angle is 67.