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The given problem is about an isosceles trapezoid \( ABCD \) with bases \( AB > CD \). The longer base \( AB \) is 20 cm, the shorter base \( CD \) is 4 cm, and the area is 96 cm². We are asked to find the degree measure of the angle between one of the non-parallel sides (legs) of the trapezoid and the larger base \( AB \).

### Step-by-step approach:

1. **Trapezoid area formula:**
   The area \( A \) of a trapezoid is given by the formula:
   \[
   A = \frac{1}{2} \times (AB + CD) \times h
   \]
   where \( AB \) and \( CD \) are the lengths of the two bases, and \( h \) is the height.

   Plugging in the values for the area and the lengths of the bases:
   \[
   96 = \frac{1}{2} \times (20 + 4) \times h
   \]
   Simplifying:
   \[
   96 = \frac{1}{2} \times 24 \times h
   \]
   \[
   96 = 12h
   \]
   Solving for \( h \):
   \[
   h = \frac{96}{12} = 8 \, \text{cm}
   \]

2. **Right triangles and trigonometry:**
   Since the trapezoid is isosceles, the non-parallel sides are equal, and the height forms right triangles with the bases. Each right triangle has a height of 8 cm and a horizontal difference:
   \[
   \text{Difference in bases} = AB - CD = 20 - 4 = 16 \, \text{cm}
   \]
   The horizontal distance is split equally between the two right triangles, so each triangle has a base of:
   \[
   \text{Base of each triangle} = \frac{16}{2} = 8 \, \text{cm}
   \]

3. **Finding the angle:**
   We can use the tangent function to find the angle \( \theta \) between the leg and the larger base \( AB \):
   \[
   \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{h}{\text{base of the right triangle}} = \frac{8}{8} = 1
   \]
   Thus, \( \theta = \tan^{-1}(1) = 45^\circ \).

### Final Answer:
The angle between the leg and the larger base of the trapezoid is \( 45^\circ \).

Would you like further clarification or details?

Here are 5 related questions to extend your understanding:
1. How does the area formula for a trapezoid differ from that of a triangle?
2. Can this method be applied to trapezoids that are not isosceles?
3. What happens to the angle if the height is increased but the bases remain the same?
4. How would the calculations change if the smaller base was larger than the height?
5. Can the legs of an isosceles trapezoid ever form a right angle with the larger base?

**Tip:** Always verify that your units and angle measures match the given information to avoid calculation errors.

Даден е равнобедрен трапец ABCD (AB > CD) с основи 20 см и 4 см и лице 96 см². Намерете градусната мярка на ъгъла, който бедрото на трапеца сключва с голямата му основа.

Solve a geometry problem involving an isosceles trapezoid with bases 20 cm and 4 cm, and an area of 96 cm². Learn how to find the angle between the leg and the larger base using trigonometry and the trapezoid area formula. Suitable for Grades 8-10.

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