Answer: ∠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
[tex]\frac{-9}{28} = \frac{28x}{28}[/tex]
[tex]-\frac{9}{28} = x[/tex]
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∠X + ∠Y + ∠Z = 180° Triangle angle sum theorem
5x + 33 + 33x + 42 + ∠Z = 180°
38x + 75 + ∠Z = 180°
-75 -75
38x + ∠Z = 105°
38[tex](-\frac{9}{28})[/tex] + ∠Z = 105°
-12.2 + ∠Z = 105°
+12.2 +12.2
∠Z = 117.2°
