Posted by Mona on Thursday, January 31, 2013 at 6:54pm.
Can you please help me with this question?
1.) Given: triangle ABC ~ triangle XYZ, m<A= 50 degrees, m<X= (2x +5y) degrees, m>Z=( 55 + y) degrees, and that m<B=(102x) degrees. Find m<Z.
Thanks.

Geometry8th gr  Reiny, Thursday, January 31, 2013 at 7:32pm
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)
= 28+x
then angle C = angle Z
28+x = 55+y
x  y = 27 or y = x27
sub that into the 1st equation
2x + 5(x27) = 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 
Geometry8th gr  Reiny, Thursday, January 31, 2013 at 7:37pm
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°
check:
angle C = 28+x = 28+185/7 = 54.4° 
Geometry8th gr  Mona, Friday, February 1, 2013 at 11:47am
Thanks!