https://file.aiquickdraw.com/mathbot/file/1727635069752rfqt7exl.jpg

The image asks you to determine the radian measure of the angle \( \theta \) using the figure provided, which shows part of a circle with a marked angle.

Here’s how you can solve this type of problem:

1. **Identify the key elements**: 
   - The figure shows a portion of a circle, with the angle \( \theta \) subtended by an arc.
   - The radius is likely 5 (based on the label near the edge of the circle), and the arc length subtended by the angle \( \theta \) is 2 (marked next to the arc).

2. **Use the formula for radians**: 
   The radian measure \( \theta \) of an angle is given by:
   \[
   \theta = \frac{s}{r}
   \]
   where:
   - \( s \) is the arc length,
   - \( r \) is the radius of the circle.

3. **Plug in the values**: 
   From the figure, \( s = 2 \) and \( r = 5 \). So:
   \[
   \theta = \frac{2}{5}
   \]

Thus, the radian measure of \( \theta \) is \( \frac{2}{5} \) radians or 0.4 radians.

Would you like more details on this process, or do you have any questions?

Here are 5 related questions:
1. What is the relationship between degrees and radians?
2. How would you convert radians into degrees?
3. What is the formula to calculate the arc length if the angle is given in radians?
4. Can the radian measure of an angle be greater than \( 2\pi \)?
5. How is the unit circle used to define radians?

**Tip**: To convert radians to degrees, multiply by \( \frac{180}{\pi} \).

Use the figure to determine the radian measure of angle θ.

Solve for the radian measure of angle θ using the formula θ = s / r, where the arc length is 2 and the radius is 5. Detailed steps provided for high school trigonometry students.

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