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In the given problem, you are asked to find the measure of \( m \angle WYV \). 

The key observations are:
- \( \angle WYV \) and \( \angle VYZ \) form a linear pair, meaning their sum is \( 180^\circ \) (since they are supplementary angles).
  
You are provided with the following equations:
- \( m \angle WYV = 6x - 12 \)
- \( m \angle VYZ = x + 16 \)

Since these angles are supplementary, we set up the equation:
\[
m \angle WYV + m \angle VYZ = 180^\circ
\]
Substituting the expressions for the angle measures:
\[
(6x - 12) + (x + 16) = 180
\]

Let's solve for \( x \).

\[
6x - 12 + x + 16 = 180
\]
\[
7x + 4 = 180
\]
\[
7x = 176
\]
\[
x = \frac{176}{7} = 25.14
\]

Now, substitute \( x = 25.14 \) into the expression for \( m \angle WYV \):

\[
m \angle WYV = 6x - 12 = 6(25.14) - 12 = 150.84 - 12 = 138.84
\]

The closest answer is 108 degrees, but based on the math, it looks like there may have been a slight error in the options provided.

Find the measure of m∠WYV, where m∠WYV = 6x - 12 and m∠VYZ = x + 16. The angles form a linear pair and are supplementary.

Solve for m∠WYV where m∠WYV = 6x - 12 and m∠VYZ = x + 16, forming a linear pair. Learn how to set up and solve the equation using algebraic techniques and the supplementary angles theorem. Suitable for Grades 8-10 students.

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