The measure of the obtuse angle in the isosceles triangle is two and a half times the measure of one base angle. What are the measures of all the angles?

##40^circ40^circand100^circ##
In an Isoceles triangle the two base angles are equal. Let the base angles be ##x##. Then the obtuse angle would be ##2 1/2*x##
We need to find the value of ##x##
Since the sum of the angles in a triangle is ##180^circ##
##rarrx+x+2 1/2*x=180^circ##
##rarr2x+2 1/2*x=180^circ##
##rarr2x+5/2*x=180^circ##
##rarr2x+(5x)/2=180^circ##
##rarr(9x)/2=180^circ##
##rarr9x=360^circ##
##color(green)(rArrx=40^circ##
Now we know that the base angles are ##color(green)(40^circ##
So the other angle is ##color(orange)(2 1/2*40=100)##