1. **State the problem:** We have angles around point G with angles labeled as $(13x)^\circ$, $38^\circ$, and $y^\circ$. We need to find the values of $x$ and $y$. 2. **Understand the geometry:** The vertical and horizontal lines intersect at G, forming four right angles of $90^\circ$ each. 3. **Use angle relationships:** The angle $(13x)^\circ$ is between the vertical line and a line through C, and $38^\circ$ is between that same line and the horizontal line. Since vertical and horizontal lines are perpendicular, the sum of these two angles must be $90^\circ$: $$ (13x)^\circ + 38^\circ = 90^\circ $$ 4. **Solve for $x$:** $$ 13x + 38 = 90 $$ $$ 13x = 90 - 38 $$ $$ 13x = 52 $$ $$ x = \frac{52}{13} $$ $$ x = 4 $$ 5. **Find $y$:** The angle $y^\circ$ is on the opposite side of the horizontal line from the $38^\circ$ angle, and since the horizontal line is straight, the angles on a straight line sum to $180^\circ$: $$ 38^\circ + y^\circ = 180^\circ $$ 6. **Solve for $y$:** $$ y = 180 - 38 $$ $$ y = 142 $$ **Final answers:** $$ x = 4 $$ $$ y = 142 $$