https://file.aiquickdraw.com/mathbot/file/17255694591636fq128fc.jpg

To find the value of \( x \), we will use the information provided in the image. The image gives us the following angles:

1. \( m\angle ABD = 124^\circ \)
2. \( m\angle ABC = 52^\circ \)
3. \( m\angle CBD = (6x + 6)^\circ \)

From the diagram, we can see that:

\[
m\angle ABD = m\angle ABC + m\angle CBD
\]

Substituting the given values:

\[
124^\circ = 52^\circ + (6x + 6)^\circ
\]

Now, let's solve for \( x \):

\[
124 = 52 + 6x + 6
\]

\[
124 = 58 + 6x
\]

\[
124 - 58 = 6x
\]

\[
66 = 6x
\]

\[
x = 11
\]

So, the value of \( x \) is \( 11 \).

Would you like further details or have any questions?

Here are some related questions that you might find interesting:

1. How do you verify the value of \( x \) using angle properties?
2. What would be the value of \( m\angle CBD \) once \( x \) is found?
3. How would the problem change if \( m\angle ABC \) was different?
4. Can you calculate the supplementary angle to \( m\angle ABD \)?
5. How can you use these angle relationships to solve for unknowns in other geometric figures?

**Tip:** When solving for unknown variables in angles, always consider the relationships between angles, such as complementary, supplementary, or angles that form a straight line.

Find the value of x given that m∠ABD = 124°, m∠ABC = 52°, and m∠CBD = (6x + 6)°.

Learn how to find the value of x when given angles m∠ABD = 124°, m∠ABC = 52°, and m∠CBD = (6x + 6)° using the angle sum property. Step-by-step solution provided for students in Grades 7-9.

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