The measure of the vertex angle of an isosceles triangle is 15 degrees more than the measure of each base angle. Find the number of degrees in each angle of the triangle.?

Let x be the measure of the base angle in degrees, so the measure of the vertex angle in degrees it will be x + 15. Since the triangle is an isosceles triangle, where the base angles are congruent, we can form the equation:

2x + (x + 15) = 180

3x + 15 = 180 subtract 15 to both sides;

3x = 165 divide by 3 to both sides;

x = 55

x + 15 = 55 + 15 = 70

Thus, each base angle is 55° and the vertex angle is 70°.