The value of the missing angles x and y are:
x = 20°
y = 70°
How to find the missing angles?
We know that Isosceles triangles have two equal sides and as such two equal base angles.
The the triangle containing the angle x is an Isosceles triangle and as such the base angles will each be x.
We also know that the sum of two opposite interior angles is equal to the sum of an exterior angle. Thus:
x + x = 40
2x = 40
x = 20°
Sum of angles in a triangle is 180 degrees. Thus:
20 + 90 + y = 180
y + 110 = 180
y = 70°