1. **Stating the problem:** We are given angles labeled as $h = 93^\circ$, $m = 122^\circ$, and need to find the values of $g$ and $k$ based on the given diagram and angle relationships. 2. **Understanding angle relationships:** In a coordinate plane with intersecting lines, angles around a point sum to $360^\circ$. Also, vertical angles (opposite angles formed by intersecting lines) are equal. 3. **Given:** - $h = 93^\circ$ - $m = 122^\circ$ 4. **Finding $g$:** Since $g$ is horizontal and $h$ is vertical, and they intersect at right angles, $g$ and $h$ are complementary angles summing to $180^\circ$ (straight line). $$g = 180^\circ - h = 180^\circ - 93^\circ = 87^\circ$$ 5. **Finding $k$:** Since $m$ and $k$ intersect and form a straight line, their angles sum to $180^\circ$. $$k = 180^\circ - m = 180^\circ - 122^\circ = 58^\circ$$ 6. **Summary of values:** - $h = 93^\circ$ - $g = 87^\circ$ - $m = 122^\circ$ - $k = 58^\circ$ These values satisfy the angle relationships in the diagram.