https://file.aiquickdraw.com/mathbot/file/172600130285779c6vv9p.jpg

The image shows two intersecting lines with labeled angles: \((2a + 3)^\circ\) and \((6a + 1)^\circ\). These angles are vertically opposite angles, meaning they are equal. 

We can set up the equation based on this property:

\[
(2a + 3) = (6a + 1)
\]

Let's solve for \(a\):

1. Subtract \(2a\) from both sides:
\[
3 = 4a + 1
\]

2. Subtract 1 from both sides:
\[
2 = 4a
\]

3. Divide by 4:
\[
a = \frac{2}{4} = \frac{1}{2}
\]

Thus, the value of \(a\) is \( \frac{1}{2} \).

Would you like further details or have any questions? Here are some related questions for practice:

1. What is the sum of the angles at a point where two lines intersect?
2. How do vertically opposite angles relate to each other?
3. What is the measure of the angle \(6a + 1\) when \(a = \frac{1}{2}\)?
4. How would the solution change if the angles were supplementary?
5. What are corresponding angles in parallel lines?

**Tip:** Always verify the nature of the angles (whether complementary, supplementary, or equal) when dealing with geometric problems.

Solve for the value of a given that (2a+3)° and (6a+1)° are vertically opposite angles.

Learn how to solve for the variable a in a vertically opposite angle problem where the angles are given as (2a+3)° and (6a+1)°. This problem demonstrates key geometric and algebraic concepts for students in Grades 7-9.

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