https://file.aiquickdraw.com/mathbot/file/1726244969680t28isx8u.jpg

Let's analyze the given image and solve for the angle \( m \angle WYV \).

### Step 1: Analyze the Given Information
- \( m \angle WYX = 40^\circ \).
- Two expressions are written for angles at point \( Y \):
  - \( \angle WYZ = 2x + 6 \) (angle adjacent to \( \angle WYX \)).
  - \( \angle VYZ = 4x - 14 \).

### Step 2: Set Up the Equation for Linear Pairs
Since \( \angle WYX \) and \( \angle WYZ \) form a linear pair (on the straight line \( XZ \)), they must sum to \( 180^\circ \).

\[
m \angle WYX + m \angle WYZ = 180^\circ
\]
Substituting the given values:

\[
40^\circ + (2x + 6) = 180^\circ
\]

### Step 3: Solve for \( x \)
Simplify the equation:

\[
40 + 2x + 6 = 180
\]
\[
2x + 46 = 180
\]
\[
2x = 180 - 46
\]
\[
2x = 134
\]
\[
x = \frac{134}{2} = 67
\]

### Step 4: Calculate the Measure of \( \angle WYV \)
Now, we substitute \( x = 67 \) into the expression for \( m \angle WYV = 4x - 14 \).

\[
m \angle WYV = 4(67) - 14
\]
\[
m \angle WYV = 268 - 14 = 254^\circ
\]

This result suggests something unusual, as \( 254^\circ \) is an obtuse angle, but angles typically do not exceed \( 180^\circ \) in typical Euclidean geometry setups. Could you verify if there's more context or if we're only focusing on angles around point \( Y \)?

Let me know if you'd like further clarification, or to go over additional details. Here are some related questions:

1. What is the sum of all angles formed around point \( Y \)?
2. Can you explain why angles in a linear pair always sum to \( 180^\circ \)?
3. How does the relationship between supplementary angles affect calculations like this one?
4. What are the properties of vertical angles that we can use in such problems?
5. If the context allowed angles larger than \( 180^\circ \), what would be the interpretation?

**Tip:** Always check if angles in linear pairs are being measured correctly to avoid exceeding \( 180^\circ \) unless the context allows it!

Find the measure of angle WYV given that m∠WYX = 40° and expressions for the adjacent angles are 2x + 6 and 4x - 14.

Learn how to solve for angle WYV using the linear pair theorem and algebraic expressions. This problem involves setting up equations based on angle relationships and solving for unknowns. Suitable for students in Grades 9-11.

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