1. **State the problem:** We have a right angle composed of two adjacent angles labeled as $(8x)^\circ$ and $(6x + 6)^\circ$. We need to write an equation to find $x$ and then solve for $x$. 2. **Recall the rule:** Adjacent angles that form a right angle sum to $90^\circ$. 3. **Write the equation:** $$8x + (6x + 6) = 90$$ 4. **Simplify the equation:** $$8x + 6x + 6 = 90$$ $$14x + 6 = 90$$ 5. **Isolate $x$:** $$14x + 6 = 90$$ $$14x = 90 - 6$$ $$14x = 84$$ 6. **Divide both sides by 14:** $$\cancel{14}x = \frac{84}{\cancel{14}}$$ $$x = 6$$ 7. **Final answer:** $$x = 6$$ This means the value of $x$ that satisfies the angle measures is 6.