Question: Solve for x in the diagram below.
$(x + 12)^\circ$
$100^\circ$
$x^\circ$
$x = \square ^\circ$
1. **State the problem:** We need to find the value of $x$ given three angles around a point: $(x + 12)^\circ$, $100^\circ$, and $x^\circ$.
2. **Important rule:** The sum of angles around a point is always $360^\circ$.
3. **Set up the equation:**
$$ (x + 12) + 100 + x = 360 $$
4. **Simplify the equation:**
$$ x + 12 + 100 + x = 360 $$
$$ 2x + 112 = 360 $$
5. **Isolate $x$:**
$$ 2x = 360 - 112 $$
$$ 2x = 248 $$
6. **Divide both sides by 2:**
$$ \cancel{2}x = \frac{248}{\cancel{2}} $$
$$ x = 124 $$
7. **Final answer:**
$$ x = 124^\circ $$