Math Problem Statement

Use the figure to find the value of x.

Solution

The image shows two intersecting lines, forming a pair of vertically opposite angles. One angle is given as (13x70)(13x - 70)^\circ, and its vertically opposite angle is 9999^\circ. Vertically opposite angles are always equal, so we can set up the equation:

13x70=9913x - 70 = 99

Now, solving for xx:

13x=99+7013x = 99 + 70 13x=16913x = 169 x=16913x = \frac{169}{13} x=13x = 13

So, the value of xx is 13\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=13x = 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!

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Math Problem Analysis

Mathematical Concepts

Algebra
Angles
Linear Equations

Formulas

Vertically opposite angles are equal

Theorems

Vertically Opposite Angle Theorem

Suitable Grade Level

Grades 8-10