Answer:
y = 144
Step-by-step explanation:
The sum of adjacent angles in a parallelogram is always 180°.
Since angle W and angle C are adjacent angles, we can find the value of x by setting the sum of their expressions equal to 180°, and solving for x:
[tex]\begin{aligned}\sf m\angle W + m\angle C &= \sf 180^{\circ}\\\\\sf 16x^{\circ} + 4x^{\circ} &= \sf 180^{\circ}\\\\\sf 16x + 4x &= \sf 180\\\\\sf 20x &= \sf 180\\\\\sf \dfrac{20x}{20}&= \sf \dfrac{180}{20}\\\\\sf x &= \sf 9\end{aligned}[/tex]
Therefore, the value of x is 9.
To find the measure of angle W, we can substitute the value of x into its expression:
[tex]\begin{aligned}\sf m\angle W &= \sf 16x^{\circ}\\\\\sf m\angle W &= \sf 16(9)^{\circ}\\\\\sf m\angle W &= \sf 144^{\circ}\end{aligned}[/tex]
Since opposite angles in a parallelogram are congruent, the measure of angle V is equal to the measure of angle W. As the measure of angle W is 144° and the measure of angle V is y°, then:
[tex]\begin{aligned}\sf y^{\circ} &= \sf 144^{\circ}\\\\\sf y &= \sf 144\end{aligned}[/tex]
Therefore, the value of y is:
[tex]\huge\boxed{\boxed{y=144}}[/tex]
