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To solve for \( x \) in the given diagram, we can use the property that the angles around point \( B \) sum up to \( 180^\circ \) since they form a straight line.

From the diagram:
- Angle \( \angle ABC = 51^\circ \)
- Angle \( \angle ABC = 3x^\circ \) (the second angle labeled in terms of \( x \))

Since the two angles form a linear pair with the horizontal line through \( B \) and \( C \), they must sum to \( 180^\circ \). Therefore, the equation is:

\[
51^\circ + 3x^\circ = 180^\circ
\]

Now, solve for \( x \):

\[
3x = 180^\circ - 51^\circ
\]
\[
3x = 129^\circ
\]
\[
x = \frac{129^\circ}{3} = 43^\circ
\]

Thus, the value of \( x \) is \( 43^\circ \).

Would you like further details or have any other questions?

Here are five related questions to explore:
1. What is the sum of angles around a point?
2. How do you identify linear pairs of angles?
3. If \( x = 43^\circ \), what is the value of \( 3x^\circ \)?
4. What is the difference between supplementary and complementary angles?
5. How can you solve for angles in a triangle using angle sum property?

**Tip:** Always check if angles form a straight line or a full circle (360°) when solving for unknowns in geometry.

Learn how to solve for x in a geometry problem where angles around a point sum to 180°. This solution applies the linear pair theorem and involves the equation 51° + 3x = 180°. Suitable for students in Grades 6-8.

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