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The image shows a problem involving a cyclic quadrilateral inscribed in a circle, where you are asked to find the measure of angle \( \angle D \).

### Given:
- \( \angle A = 108^\circ \)
- \( \angle B = 94^\circ \)
- \( \angle C = 98^\circ \)

To find \( \angle D \), we use the **cyclic quadrilateral angle theorem**:
- The opposite angles of a cyclic quadrilateral sum to \( 180^\circ \).

### Step-by-step solution:
1. \( \angle A \) and \( \angle C \) are opposite angles, so:
   \[
   \angle A + \angle C = 180^\circ
   \]
   \[
   108^\circ + 98^\circ = 180^\circ
   \]
   This confirms the relationship holds for these angles.

2. Now, to find \( \angle D \), use the same theorem for angles \( \angle B \) and \( \angle D \):
   \[
   \angle B + \angle D = 180^\circ
   \]
   \[
   94^\circ + \angle D = 180^\circ
   \]
   Solving for \( \angle D \):
   \[
   \angle D = 180^\circ - 94^\circ = 86^\circ
   \]

### Answer:
\( \angle D = 86^\circ \).

Let me know if you'd like further details or clarifications. Here are some related questions to explore:

1. How do you prove the cyclic quadrilateral angle theorem?
2. What happens if the quadrilateral is not cyclic (not inscribed in a circle)?
3. Can all quadrilaterals be inscribed in a circle?
4. How do inscribed angles relate to arc measures in a circle?
5. What is the sum of interior angles for any quadrilateral?

**Tip:** Always check if a quadrilateral is cyclic to apply special angle properties.

Find the measure of angle D in a cyclic quadrilateral inscribed in a circle, given angles A = 108°, B = 94°, and C = 98°.

Learn how to find the measure of angle D in a cyclic quadrilateral inscribed in a circle, given the other angles: A = 108°, B = 94°, and C = 98°. This problem applies the cyclic quadrilateral angle theorem. Suitable for students in Grades 8-10.

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