Math Problem Statement

Find x

Find x

Solution

The image shows a pair of vertically opposite angles, one labeled as 4x+104x + 10^\circ and the other as xx. Since vertically opposite angles are always equal, we can set the two expressions equal to each other.

4x+10=x4x + 10^\circ = x

Now, let's solve for xx.

  1. Subtract xx from both sides:

4xx+10=xx4x - x + 10^\circ = x - x

3x+10=03x + 10^\circ = 0

  1. Subtract 10° from both sides:

3x=103x = -10^\circ

  1. Divide by 3:

x=103x = \frac{-10^\circ}{3}

x=1033.33x = -\frac{10}{3}^\circ \approx -3.33^\circ

So, x3.33x \approx -3.33^\circ.

Would you like more details on this solution, or have any further questions?

Here are 5 related questions to deepen your understanding:

  1. What are vertically opposite angles, and why are they always equal?
  2. How would the solution change if the angles were adjacent instead of opposite?
  3. What is the sum of angles in a straight line, and how does that property help in angle problems?
  4. How would you solve for xx if both angles were expressed in terms of variables?
  5. Why is solving for xx important in understanding the properties of angles?

Tip: In geometry problems, recognizing angle relationships such as vertical angles, corresponding angles, or alternate angles often leads directly to equations that are easier to solve!

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Math Problem Analysis

Mathematical Concepts

Algebra
Geometry
Vertically Opposite Angles

Formulas

4x + 10° = x

Theorems

Vertically Opposite Angles Theorem

Suitable Grade Level

Grades 7-9