triangle xyz is isosceles with < z as the vertex angle.  if < x = 5x+33, < y = 33x+42,  find < z

∠Z = 117.2°

Step-by-step explanation:

∠X and ∠Y are isosceles so they are congruent (equal to each other)

5x + 33 = 33x + 42

-5x           -5x          

         33 = 28x + 42

        -42            -42

        -9   =  28x

************************************************************

∠X + ∠Y + ∠Z = 180°                Triangle angle sum theorem

5x + 33 + 33x + 42 + ∠Z = 180°

38x + 75 + ∠Z = 180°

        -75              -75

38x          + ∠Z = 105°

38      + ∠Z = 105°

-12.2         + ∠Z = 105°

+12.2                     +12.2

                     ∠Z = 117.2°

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