Question

How do you find the measures of the angles of an isosceles triangle if the measure of the vertex angle is 40 degrees less than the sum of the measures of the base angles?

Answer 1

let one of the base angle be x°

the other base angle is also same = x°

the vertex angle is 2x° - 40°

sum of angles in triangle = 180°

x + x + 2x - 40 = 180°

4x - 40 = 180°

4x = 180 + 40 = 220°

x = 220/4

x = 55°

therefore the base angles are 55° and 55°

the vertex angle is

2x - 40 = 2×55 - 40 = 110 - 40 = 70°