https://file.aiquickdraw.com/mathbot/file/1726669814423xff30nn8.jpg

Given that \( \overrightarrow{BD} \) bisects \( \angle ABC \), it means that \( \angle ABD \) and \( \angle DBC \) are equal. This gives us the equation:

\[
\angle ABD = \angle DBC
\]

From the image:
- \( \angle ABD = (3x - 7)^\circ \)
- \( \angle DBC = 20^\circ \)

Since \( \overrightarrow{BD} \) bisects \( \angle ABC \), we can set up the equation:

\[
3x - 7 = 20
\]

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

1. Add 7 to both sides of the equation:

\[
3x = 27
\]

2. Divide by 3:

\[
x = 9
\]

So, the value of \( x \) is \( 9 \).

Would you like more details or have any questions about this solution?

Here are 5 related questions that build on this information:
1. What is the measure of \( \angle ABC \) in the diagram?
2. How do you find the measure of an angle when given an algebraic expression?
3. How can you check if a line truly bisects an angle?
4. What is the importance of angle bisectors in triangle properties?
5. How can this concept of angle bisectors be applied in real-life scenarios?

**Tip:** In geometry, when a line bisects an angle, it divides the angle into two equal parts, which is a helpful property for solving various problems.

BD bisects ∠ABC. Write an equation and solve for the value of x.

Learn how to solve a problem involving an angle bisector in a geometric figure. This problem demonstrates setting up an equation based on the properties of bisected angles. Suitable for students in Grades 8-10.

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