If A and B are vertical angles, and A = (11x - 5)°, and B = (6x + 20)°, find x.Question 3Select one:a.5b.4c.25d.19

Step 1: Break Down the Problem

We need to find the value of $x$ given that angles $A$ and $B$ are vertical angles. Since vertical angles are equal, we can set up the equation:

$A = B$

Step 2: Relevant Concepts

From the problem, we have:

• $A = 11x - 5$
• $B = 6x + 20$

Setting them equal gives us the equation:

$11x - 5 = 6x + 20$

Step 3: Analysis and Detail

Now, we will solve for $x$:

1. Subtract $6x$ from both sides: $11x - 6x - 5 = 20 \\ 5x - 5 = 20$

2. Add $5$ to both sides: $5x = 25$

3. Divide by $5$: $x = 5$

Step 4: Verify and Summarize

We will verify by substituting $x = 5$ back into the expressions for $A$ and $B$:

• For angle $A$: $A = 11(5) - 5 = 55 - 5 = 50°$

• For angle $B$: $B = 6(5) + 20 = 30 + 20 = 50°$

Since both angles are equal, our solution is verified.

Final Answer

The value of $x$ is $\boxed{5}$.