This problem involves a geometric figure inside a circle with a central angle and an inscribed angle. We are asked to determine the size of the central angle $\angle POQ$.

Key Information:

• $\angle PRQ$ is an inscribed angle, and its value is given as $29^\circ$.
• $O$ is the center of the circle, making $\angle POQ$ a central angle.

Inscribed Angle Theorem:

The inscribed angle $\angle PRQ$ is half the measure of the central angle $\angle POQ$ that subtends the same arc. Therefore, we can use the following relationship:

$\text{Central Angle } (\angle POQ) = 2 \times \text{Inscribed Angle } (\angle PRQ)$

Calculation:

$\angle POQ = 2 \times 29^\circ = 58^\circ$

Thus, the measure of $\angle POQ$ is 58°.

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5 Related Questions:

1. What is the Inscribed Angle Theorem, and how does it apply to other types of problems?
2. How do you calculate angles formed by chords in a circle?
3. What is the relationship between a central angle and its corresponding arc length?
4. How can the properties of circles be used to solve problems involving tangents?
5. How do you solve problems involving cyclic quadrilaterals?

Tip:

When dealing with angles in circles, always remember the Inscribed Angle Theorem—an inscribed angle is half the central angle that subtends the same arc.