To solve for the missing angles $g$, $h$, $k$, and $m$, we can use properties of intersecting lines and supplementary angles.

Step-by-step explanation:

1. Angle $h$ is already provided as $112^\circ$. Since $g$ and $h$ are vertically opposite angles (because two lines intersect at a point), we know: $g = h = 112^\circ$

2. Angle $m$ is given as $92^\circ$. Angles $m$ and $k$ are on a straight line, meaning they are supplementary angles. Supplementary angles add up to $180^\circ$. Therefore: $k + m = 180^\circ$ Substituting $m = 92^\circ$: $k + 92^\circ = 180^\circ$ Solving for $k$: $k = 180^\circ - 92^\circ = 88^\circ$

Summary of the missing angles:

• $g = 112^\circ$
• $h = 112^\circ$ (given)
• $k = 88^\circ$
• $m = 92^\circ$ (given)

Would you like further details or have any questions?

Here are 5 related questions to expand your understanding:

1. What are the properties of vertically opposite angles?
2. How do supplementary angles work with intersecting lines?
3. Can angles be complementary, and if so, how are they different from supplementary angles?
4. How would this change if you had parallel lines intersected by a transversal?
5. What is the sum of the interior angles in a triangle, and how can this concept be applied to more complex shapes?

Tip: Vertically opposite angles are always equal when two lines intersect!