We get that Y=75 because the triangle is isoceles and (180-30)/2=75 we make a new iscoeles triangle where that Y is an angle.We find out that the angle is 30 degrees by similar triangles and subtract 80-30 to get 50 then we do 50*2=100 and we finally do 180-100=80 to get X=80 so X+Y=80+75=155 so at last the answer is X+Y=155
If I am not correct then it is:
We get that Y=75 because the triangle is isoceles and (180-30)/2=75 we make a new iscoeles triangle where that Y is an angle.We find out that the angle is 30 degrees by similar triangles and subtract 77.5-30 to get 47.5 then we do 47.5*2=95 and we finally do 180-95=75 to get X=75 so X+Y=75+75=150 so at last the answer is X+Y=150