The problem provides an inscribed angle of $2x + 5$ degrees and an arc measure of $29^\circ$ for a circle, with the goal of finding $x$.

Solution

1. In a circle, the measure of an inscribed angle is half the measure of the intercepted arc.
2. Here, the inscribed angle is $2x + 5$ and it intercepts an arc measuring $29^\circ$.

Using the inscribed angle theorem: $2x + 5 = \frac{29}{2}$

Solving for $x$

1. Start by simplifying: $2x + 5 = 14.5$

2. Subtract 5 from both sides: $2x = 9.5$

3. Divide by 2: $x = 4.75$

Conclusion

The correct answer is: Option 3) $x = 4.75$

Would you like more details on the inscribed angle theorem or have other questions?

Here are some related questions to deepen understanding:

1. What is the inscribed angle theorem, and how does it apply to other circle problems?
2. How can the inscribed angle theorem be used to find arc lengths in other scenarios?
3. Can we apply the inscribed angle theorem to find an angle if we know the arc length?
4. How would the solution change if the arc measure was different?
5. What is the difference between an inscribed angle and a central angle in a circle?

Tip: Always verify which arc or angle you're working with; they often lead to different relationships in circle theorems.