https://file.aiquickdraw.com/mathbot/file/17256757413052s7tc7bi.jpg

To solve for the value of \( a \), we need to use the fact that the sum of the angles around a point is \( 180^\circ \). From the image, we can see that the angles given are \( 52^\circ \), \( (8a + 6)^\circ \), and the right angle, which is \( 90^\circ \).

The equation is:

\[
52^\circ + (8a + 6)^\circ + 90^\circ = 180^\circ
\]

Simplify the equation:

\[
52 + 8a + 6 + 90 = 180
\]

\[
8a + 148 = 180
\]

Subtract 148 from both sides:

\[
8a = 180 - 148
\]

\[
8a = 32
\]

Divide by 8:

\[
a = 4
\]

### Solution:
The value of \( a \) is \( 4 \).

Would you like more details or have any questions?

Here are some related questions:
1. How do you solve equations with multiple variables?
2. What are complementary and supplementary angles?
3. How can we use algebra in geometry problems?
4. What is the importance of knowing angle relationships?
5. How do you find unknown angles in different geometric figures?

**Tip:** Always check the sum of angles in various shapes; for example, the angles around a point sum to \( 360^\circ \), while in a triangle, they sum to \( 180^\circ \).

Solve for the value of a in the diagram where the angles given are 52°, (8a + 6)°, and a right angle.

Learn how to solve for the variable 'a' in a right-angle diagram, where the given angles sum to 180°. This example involves algebra and geometry concepts, including the sum of angles and the right-angle theorem. Suitable for students in Grades 7-9.

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