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=(102-x) degrees. Find m<Z.

Thanks.

- Geometry-8th 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 = 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

- Geometry-8th 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°

- Geometry-8th gr -
**Mona**, Friday, February 1, 2013 at 11:47am
Thanks!

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