If     A and     B are vertical angles, and     A = (2x - 11)° , and     B = (x + 7)°, find x.

1. Break Down the Problem

To find the value of $x$, we start by stating that vertical angles are equal. Therefore, we can set the expressions for angles $A$ and $B$ equal to each other: $(2x - 11)° = (x + 7)°$

2. Relevant Concepts

Since $A$ and $B$ are equal, we will use the equation derived from their equality to solve for $x$.

3. Analysis and Detail

Now, let's solve the equation step-by-step:

1. Set the equations equal: $2x - 11 = x + 7$

2. Subtract $x$ from both sides: $2x - x - 11 = 7$ This simplifies to: $x - 11 = 7$

3. Add 11 to both sides: $x = 7 + 11$ This simplifies to: $x = 18$

4. Verify and Summarize

We can verify by substituting $x = 18$ back into the expressions for $A$ and $B$:

• For $A$: $A = 2(18) - 11 = 36 - 11 = 25°$

• For $B$: $B = 18 + 7 = 25°$

Both angles are indeed equal, confirming our solution is correct.

Final Answer

The value of $x$ is $\boxed{18}$.