given that triangle ABC~ triangle XYZ, angle a=50, angle x=(2x+5y), angle z= (5x+y), and that angle b =(102-x), find angle z.

Answer 1

since the triangles are similar, we know that the angles

A=X, B=Y, C=Z

So,

2x+5y = 50
Y = 102-x
C = 5x+y

Also, the angles have to add up to 180. So,

50+(102-x)+C = 180
(2x+5y)+Y+(5x+y) = 180

Putting all that together, you can get

50+102-x+5x+y = 180
2x+5y+102-x+5x+y = 180

or,

4x+y = 28
6x+6y = 78

x=5
y=8
So, we get

A=50
B=97
C=33

X=50
Y=97
Z=33

Answer 2

nope