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The problem you provided involves a circular pizza with a diameter of 16 inches that is cut into slices. It gives the angle \( \angle BAC = 45^\circ \) and asks to find the value of \( x \), which represents the length of arc \( BC \).

### Given:
- Diameter of the pizza: 16 inches → Radius \( r = 8 \) inches.
- Central angle \( \angle BAC = 45^\circ \).
- The length of arc \( BC = x \).

### Solution Steps:
The formula for the length of an arc is:
\[
\text{Arc length} = \theta \cdot r
\]
where:
- \( \theta \) is the central angle in radians.
- \( r \) is the radius of the circle.

#### Step 1: Convert the angle to radians
To convert the angle from degrees to radians, use the conversion factor \( \frac{\pi}{180^\circ} \):
\[
\theta = 45^\circ \times \frac{\pi}{180^\circ} = \frac{\pi}{4} \text{ radians}.
\]

#### Step 2: Calculate the arc length
Now, using the formula for arc length:
\[
\text{Arc length} = \theta \cdot r = \frac{\pi}{4} \times 8 = 2\pi \text{ inches}.
\]

Thus, the length of arc \( BC \) is \( 2\pi \) inches.

### Final Answer:
The value of \( x \) is \( 2\pi \) inches.

Would you like a more detailed explanation of any of the steps? 

Here are 5 related questions to expand on this topic:
1. How do you calculate the area of a sector with a given central angle?
2. What is the total circumference of the pizza if the diameter is 16 inches?
3. How do you convert between degrees and radians for other angles?
4. How would the arc length change if the central angle were doubled?
5. How do you find the length of a chord given the central angle and radius?

**Tip:** Always remember to convert degrees to radians when using formulas involving arc length or sector area.

A circular pizza with a diameter of 16 inches is cut into slices as shown in the figure. If the measure of angle ∠BAC is 45° and the length of arc BC is xπ inches, then what is the value of x?

This problem involves finding the arc length in a circle with a diameter of 16 inches and a central angle of 45°. It requires using formulas for converting degrees to radians and calculating arc length.

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