Let's analyze the problem step by step.

Given:

• A circle with a central angle of 44°.
• The angles x, y, and z are marked inside the circle.
• The diagram suggests that x, y, and z are angles in an isosceles triangle, where the center O is involved.

Observations:

1. Central Angle Theorem states that an inscribed angle subtended by the same arc is half the central angle.

   • Here, y and z are inscribed angles subtended by the same arc as the given 44° central angle.
   • Therefore, y = z = 68° because $180° - 44° = 136°$, and each angle at the circumference is half of this.

2. x is opposite to y in the same triangle, making $x = 68°$.

Correct Answer:

$x = 68°, \quad y = 68°, \quad z = 68°$ The correct option is C.

Would you like a deeper explanation or any clarifications?

Related Questions:

1. What is the Inscribed Angle Theorem, and how does it apply here?
2. How can we use the Cyclic Quadrilateral Theorem in circle geometry?
3. What happens if the given central angle were different?
4. How do you find missing angles in a semi-circle?
5. Why is a diameter important in circle theorems?

Tip:

In circle problems, always look for inscribed angles, central angles, and cyclic quadrilateral properties to simplify your solution!