If A and B are supplementary, and A = (2x - 6)°, and B = (x + 12)°, find x.Question 51Select one:a.58b.62c.27d.3

1. Break Down the Problem

We are given that angles $A$ and $B$ are supplementary. This means that the sum of angles $A$ and $B$ equals $180^\circ$. We need to find the value of $x$ given the expressions for angles $A$ and $B$.

2. Relevant Concepts

The definition of supplementary angles can be expressed mathematically as: $A + B = 180^\circ$ Substituting the given expressions for angles $A$ and $B$: $(2x - 6) + (x + 12) = 180$

3. Analysis and Detail

Now, we can combine the expressions and solve for $x$:

1. Combine the terms on the left side: $2x - 6 + x + 12 = 180$ This simplifies to: $3x + 6 = 180$

2. Subtract 6 from both sides: $3x = 180 - 6$ Simplifying gives: $3x = 174$

3. Divide both sides by 3: $x = \frac{174}{3}$ Thus: $x = 58$

4. Verify and Summarize

To verify, we can substitute $x = 58$ back into the expressions for $A$ and $B$:

• Calculate $A$: $A = 2(58) - 6 = 116 - 6 = 110^\circ$
• Calculate $B$: $B = 58 + 12 = 70^\circ$

Now, check if $A + B = 180^\circ$: $110 + 70 = 180^\circ$

This confirms our calculation is correct.

Final Answer

The value of $x$ is $\boxed{58}$.