Geometry-8th gr

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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 -

    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 -

    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 -

    Thanks!

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