The measure of the obtuse angle in the isosceles triangle is two and a half times the measure of one base angle. write and solve a system of linear equations to find the measures of all the angles.

Let the base angle be x. If the obtuse angle is two and a half times the base angle, it will be 2.5x. In a triangle, all three angles will add up to 180. The third angle, the other base angle will be equal to x. So the equation will be:

x + x + 2.5x = 180
2x + 2.5x = 180
4.5x = 180
x = 40

If x = 40, then 2.5x = 100