[tex]\bold {QUESTION:}[/tex]
Quadrilateral MACY is a parallelogram. If m∠A=x and m∠C= (2x-30), then m∠Y?
[tex]\bold {SOLUTION:}[/tex]
Since we are given m∠A and m∠C, we will use their relationship to find x. The two angles are consecutive angles so they are supplementary, thus,
[tex] \large \tt m∠A + ∠C = 180° \\ \\ \large \tt (x) + (2x - 30) = 180 \\ \\ \large \tt 3x - 30 = 180 \\ \\ \large \tt 3x = 180 + 30 \\ \\ \large \tt \frac{3x}{3} = \frac{210}{3} \\ \\ \large \boxed{\tt x = 70}[/tex]
Now we will equate m∠Y and m∠C since they are congruent because they are opposite angles.
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \large \tt m∠Y=m∠C \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \large \tt m∠Y = x \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \large\red{\boxed{\tt m∠Y=70°}} [/tex]
[tex]\\ \\[/tex]
#CarryOnLearning
