x = 115
y = 115
z = 25
If AB is parallel to CD and CD is parallel to EF then AB is parallel to EF. If EA is perpendicular to AB, then it is also perpendicular to EF. This means that <AEF = 90°. <BEF and <AEB are complementary angles, meaning they add up to 90°. <BEF = 65°, so:
<AEF - <BEF = <AEB (this solves z)
90° - 65° = 25°
z = 25
EA is perpendicular to AB. This means that <EAB = 90°. A triangle is 180°, so:
<ABE = (180° - <EAB - <AEB(value z))
<ABE = 180° - 90° - 25° = 65°
this is the value for <CDE as they are similar triangles. This means that x and y have the same value.
<ABE and <x are supplementary angles, as are <CDE and <y. This means that the sum of the two is 180°. To find x:
<x = 180° - <ABE
<x = 180° - 65° = 115°
x = 115
x and y have the same value, so y = 115
Therefore,
x = 115
y = 115
z = 25
