https://file.aiquickdraw.com/mathbot/file/1726008147395otbq22lb.jpg

Let's analyze the given image to solve for \( x \) and \( y \).

We are given two pairs of vertically opposite angles. Vertically opposite angles are always equal. Based on the diagram:

1. The angle labeled \( (28 + x)^\circ \) is vertically opposite to the angle labeled \( (3x)^\circ \).
2. The angle labeled \( y^\circ \) is vertically opposite to another angle, but we can focus on the first relationship to solve for \( x \).

Since these are vertically opposite angles:
\[
28 + x = 3x
\]
Now, let's solve this equation for \( x \).

\[
28 = 3x - x
\]
\[
28 = 2x
\]
\[
x = \frac{28}{2} = 14
\]

Now that we know \( x = 14 \), we can substitute this value back into the angle labeled \( (28 + x)^\circ \) to calculate the size of that angle:

\[
28 + x = 28 + 14 = 42^\circ
\]

Thus, the value of \( y^\circ \) (since it is vertically opposite to this angle) is also \( 42^\circ \).

Therefore:
- \( x = 14 \)
- \( y = 42 \)

Would you like any further clarification or additional details?

Here are 5 related questions:
1. What are vertically opposite angles, and why are they always equal?
2. Can this method of solving for angles be used with parallel lines and transversals?
3. How would the problem change if the angles were supplementary instead of vertically opposite?
4. What is the general approach to solving systems of equations with two variables?
5. How can you verify your answer using a protractor or other geometric tools?

**Tip:** Always look for relationships like vertical angles, supplementary angles, or corresponding angles when solving geometry problems involving intersecting lines.

Solve for x and y in the given system of vertically opposite angles: (28 + x)° and (3x)°.

Learn how to solve for x and y in a problem involving vertically opposite angles. This step-by-step solution involves algebraic manipulation and the Vertically Opposite Angles Theorem. Suitable for students in Grades 7-9.

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