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To solve these problems, we need to find the central angle of each sector based on the arc length and the radius of the circle. The formula to find the central angle \( \theta \) in degrees is:

\[
\theta = \left( \frac{\text{arc length}}{2 \pi \times \text{radius}} \right) \times 360^\circ
\]

Let's solve each one step by step:

### 1. Problem 1
- Arc length = 26.4 cm
- Radius = 21 cm

\[
\theta = \left( \frac{26.4}{2 \pi \times 21} \right) \times 360^\circ
\approx \left( \frac{26.4}{131.95} \right) \times 360^\circ
\approx 72.04^\circ
\]

### 2. Problem 2
- Arc length = 94.2 cm
- Radius = 45 cm

\[
\theta = \left( \frac{94.2}{2 \pi \times 45} \right) \times 360^\circ
\approx \left( \frac{94.2}{282.74} \right) \times 360^\circ
\approx 119.92^\circ
\]

### 3. Problem 3
- Arc length = 157 cm
- Radius = 90 cm

\[
\theta = \left( \frac{157}{2 \pi \times 90} \right) \times 360^\circ
\approx \left( \frac{157}{565.49} \right) \times 360^\circ
\approx 99.94^\circ
\]

### 4. Problem 4
- Arc length = 176 cm
- Radius = 63 cm

\[
\theta = \left( \frac{176}{2 \pi \times 63} \right) \times 360^\circ
\approx \left( \frac{176}{395.84} \right) \times 360^\circ
\approx 160.09^\circ
\]

### 5. Problem 5
- Arc length = 55 cm
- Radius = 35 cm

\[
\theta = \left( \frac{55}{2 \pi \times 35} \right) \times 360^\circ
\approx \left( \frac{55}{219.91} \right) \times 360^\circ
\approx 90.06^\circ
\]

### 6. Problem 6
- Arc length = 60 cm
- Radius = 31.4 cm

\[
\theta = \left( \frac{60}{2 \pi \times 31.4} \right) \times 360^\circ
\approx \left( \frac{60}{197.19} \right) \times 360^\circ
\approx 109.54^\circ
\]

If you need more details or have questions, feel free to ask!

### Related Questions:
1. How do we find the arc length if the central angle and radius are given?
2. What is the formula for calculating the area of a sector in a circle?
3. How does changing the radius of a circle affect the arc length for the same central angle?
4. Can we convert the central angle from degrees to radians? What is the process?
5. How is the concept of arc length applied in real-world problems?

### Tip:
Always ensure the units of radius and arc length are consistent when solving problems involving circles.

Tentukan besar sudut juring pada lingkaran-lingkaran berikut.

Learn how to determine the central angle of a circle sector using arc length and radius. This step-by-step solution includes example problems and detailed calculations, suitable for students in Grades 8-10.

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