The image shows a geometric figure that appears to be a kite with angles labeled and a common vertex at the bottom. The angles at the base of the kite are labeled as $x$ degrees and the top angle as 96 degrees.

Problem Breakdown:

1. A kite is a quadrilateral with two distinct pairs of adjacent sides that are equal.
2. The sum of the interior angles in any quadrilateral is $360^\circ$.
3. In a kite, the angles between the unequal sides are equal.

Given:

• Top angle: $96^\circ$
• Bottom angles: $x$ (both angles)

Solution:

Let the angle at the top be $\angle A = 96^\circ$, and the angles at the bottom be $\angle B = \angle D = x^\circ$.

The sum of all angles in the quadrilateral is: $\angle A + \angle B + \angle C + \angle D = 360^\circ$

Given the symmetry of the kite: $\angle B = \angle D = x^\circ$ So: $\angle C = x^\circ$

Now substitute the known values: $96^\circ + x^\circ + x^\circ + x^\circ = 360^\circ$ Simplifying this: $96^\circ + 3x^\circ = 360^\circ$ $3x^\circ = 360^\circ - 96^\circ$ $3x^\circ = 264^\circ$ $x^\circ = \frac{264^\circ}{3}$ $x^\circ = 88^\circ$

Answer:

The value of $x$ is $88^\circ$.

Would you like more details on any step, or have any questions?

Follow-up Questions:

1. What are the properties of a kite in terms of its sides and angles?
2. How do you calculate the sum of interior angles for any polygon?
3. How can you verify if the sides of a quadrilateral are equal?
4. Can the angles in a kite ever be all equal? Why or why not?
5. What is the relationship between the diagonals in a kite?

Tip:

When dealing with any polygon, remember that the sum of the interior angles is given by $(n-2) \times 180^\circ$, where $n$ is the number of sides.