https://file.aiquickdraw.com/mathbot/file/1725548425198rzz4fkl4.jpg

The image shows two intersecting lines, forming a pair of vertically opposite angles. One angle is given as \( (13x - 70)^\circ \), and its vertically opposite angle is \( 99^\circ \). Vertically opposite angles are always equal, so we can set up the equation:

\[
13x - 70 = 99
\]

Now, solving for \( x \):

\[
13x = 99 + 70
\]
\[
13x = 169
\]
\[
x = \frac{169}{13}
\]
\[
x = 13
\]

So, the value of \( x \) is \( \boxed{13} \).

Would you like further details or explanations on any part of this solution?

Here are five questions you might find interesting:
1. How do vertically opposite angles help in solving such problems?
2. What are other angle properties in intersecting lines?
3. Can supplementary angles be used in this problem?
4. How can we verify that \( x = 13 \) is correct?
5. What if the angles were complementary or supplementary? How would that affect the equation?

**Tip:** Always check if the problem involves vertically opposite angles when two lines intersect—they are always equal!

Learn how to solve for x using the property of vertically opposite angles in intersecting lines. In this problem, we use algebra to find the value of x, with one angle expressed as (13x - 70)° and the opposite angle as 99°. Suitable for students in Grades 8-10.

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