The value of x and y in the Isosceles triangles are 26° and 45° respectively.
The base angles of an Isosceles triangle are equal in measure, and the sum of interior angles is equal to 180°.
Considering the Isosceles right triangle, we can get the value of y as follows:
90° + 2y = 180°
2y = 180° - 90° {collect like terms}
2y = 90°
y = 90°/2 {divide through by 2}
y = 45°
Considering the biggee Isosceles triangle, one of its base angles is (x + y) thus we have that:
38° + 2(x + y) = 180°
38° + 2(x + 45°) = 180°
38° + 2x + 90° = 180°
2x + 128° = 180°
2x = 180° - 128°
2x = 52°
x = 52°/2
x = 26°.
Therefore, the measure of x and y are derived to be 26° and 45° respectively.