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In the image you provided, there is a geometric figure involving angle relationships. Vertex \( V \) forms angles with three other points, \( X \), \( Y \), and \( W \). Specifically:

- \( \angle YVX = 5x + 13 \) 
- \( \angle WVX = 7x - 1 \)

Since these two angles appear to form a straight angle (a right angle is marked between them), they should sum to 90° because they are complementary angles.

To solve for \( x \):

\[
(5x + 13) + (7x - 1) = 90
\]

Now let's solve for \( x \):

\[
5x + 13 + 7x - 1 = 90
\]

\[
12x + 12 = 90
\]

\[
12x = 90 - 12
\]

\[
12x = 78
\]

\[
x = \frac{78}{12} = 6.5
\]

So, \( x = 6.5 \).

### Now that we know \( x \), we can calculate the angles:

1. \( \angle YVX = 5x + 13 = 5(6.5) + 13 = 32.5 + 13 = 45.5^\circ \)
2. \( \angle WVX = 7x - 1 = 7(6.5) - 1 = 45.5^\circ \)

Both angles sum to \( 45.5^\circ + 45.5^\circ = 90^\circ \), confirming the complementary relationship.

Would you like more details or have any questions about this solution? 

Here are 5 related questions for practice:

1. If \( x \) were 10, what would the value of \( \angle YVX \) and \( \angle WVX \) be?
2. What is the sum of two angles if they form a straight angle?
3. How would the angles change if they were supplementary instead of complementary?
4. What happens to the value of \( x \) if both angle expressions were increased by 5?
5. If the angle at \( V \) formed a complete circle, what would the total degrees sum up to?

**Tip**: Always check for geometric relationships, like complementary or supplementary angles, when solving for unknowns in geometry.

In the image you provided, there is a geometric figure involving angle relationships. Vertex V forms angles with three other points, X, Y, and W. Specifically: - ∠YVX = 5x + 13 - ∠WVX = 7x - 1. Solve for x and the corresponding angles.

Learn how to solve for x in the angle expressions 5x + 13 and 7x - 1 when they are complementary, summing to 90 degrees. This problem involves algebra and geometry, and is suitable for students in Grades 8-10.

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