https://file.aiquickdraw.com/mathbot/file/1726067859759vqr74jpq.jpg

The image shows a pair of intersecting lines with two given expressions: \( x + 14 \) and \( 5x - 74 \), representing vertical angles.

Vertical angles are always congruent, meaning that:

\[
x + 14 = 5x - 74
\]

Let's solve this equation step by step:

1. Subtract \( x \) from both sides:

\[
14 = 4x - 74
\]

2. Add 74 to both sides:

\[
14 + 74 = 4x
\]

\[
88 = 4x
\]

3. Divide both sides by 4:

\[
x = \frac{88}{4} = 22
\]

Thus, \( x = 22 \).

Would you like further clarification on any step? Here are some related questions to explore:

1. What are vertical angles, and why are they congruent?
2. How can we check if the solution \( x = 22 \) is correct?
3. What happens if the lines were parallel? Would the same rule apply?
4. What other properties of angles formed by intersecting lines can we use?
5. How can we solve similar problems involving supplementary angles?

**Tip**: When solving equations, always double-check by substituting the value back into the original equation.

Solve for x in the given diagram where the expressions x + 14 and 5x - 74 are vertical angles.

Learn how to solve for x using vertical angles with the equation x + 14 = 5x - 74. This example demonstrates key algebraic steps to find the value of x by applying the Vertical Angles Theorem. Suitable for students in Grades 7-9.

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