This is a geometry problem involving angles in a rectangle with diagonals drawn. Let's break it down:

Given Information:

1. The rectangle has diagonals crossing at the center.
2. $g = 110^\circ$ (angle formed by diagonals).
3. The rectangle divides into smaller angles labeled $f, h, k$, each near a corner.

Key Properties:

• The diagonals of a rectangle bisect each other and the opposite angles.
• Angles formed by the diagonals add up to $180^\circ$ for adjacent angles at the crossing.

Solving:

1. $g = 110^\circ$: This is given.
2. $h$: Since $h$ and $g$ are supplementary (angles on a straight line), $h = 180^\circ - 110^\circ = 70^\circ$.
3. $f$: This is one of the smaller angles split by the diagonals. Since the diagonals bisect the corner angle of the rectangle ($90^\circ$): $f = \frac{90^\circ}{2} = 45^\circ.$
4. $k$: By symmetry, $k$ also equals $45^\circ$ (opposite corners have equal angles in a rectangle).

Final Answers:

• $f = 45^\circ$
• $g = 110^\circ$ (given)
• $h = 70^\circ$
• $k = 45^\circ$

Would you like further clarification on any step?

Related Questions:

1. Why are the diagonals of a rectangle always congruent?
2. What would change if this was a rhombus instead of a rectangle?
3. How can this concept apply to solving parallelogram problems?
4. How do you calculate angles in polygons formed by diagonals?
5. What are supplementary and complementary angles, and how are they used here?

Tip: When solving geometry problems, always look for properties like symmetry, bisectors, or relationships between angles.