In similar triangles, the corresponding angles are equal, so angle A = angle x
2x+5y = 50
in triangle ABC, angle C = 180 - 50 - (102 - x)
then angle C = angle Z
28+x = 55+y
x - y = 27 or y = x-27
sub that into the 1st equation
2x + 5(x-27) = 50
7x = 50+135
x = 185/7 °
then y = 185/7 - 27 = -4/7
something quite wrong here !
I assumed you listed the points in corresponding order, so
angle A = angle X
angle B = angle Y
angle C = angle Z
that is why I had to first find angle C
ahhh, but y is not the size of the angle, Z is
angle Z = 55 + y
= 55 - 4/7 = 381/7° or appr 54.4°
angle C = 28+x = 28+185/7 = 54.4°
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