1. **State the problem:** We are given two adjacent angles at point G on a straight line: one angle measures $8x$ degrees and the other measures 60 degrees. We need to write an equation using angle relationships and solve for $x$. 2. **Formula and rules:** Adjacent angles on a straight line are supplementary, meaning their measures add up to 180 degrees. 3. **Write the equation:** Since the two angles are adjacent on a straight line, we have: $$8x + 60 = 180$$ 4. **Solve for $x$:** $$8x + 60 = 180$$ Subtract 60 from both sides: $$8x + \cancel{60} - \cancel{60} = 180 - 60$$ $$8x = 120$$ Divide both sides by 8: $$\frac{8x}{\cancel{8}} = \frac{120}{\cancel{8}}$$ $$x = 15$$ 5. **Answer:** The value of $x$ is 15.