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.