Find the degree measure of the angle subtended at the centre of a circle of radius 100 cm by an arc of length 22 cm. (Use π= 22/7)

Answer

To find the degree measure of the angle subtended at the center of a circle by an arc of length 22 cm, we can follow these steps:

### Step 1: Understand the formula for arc length
The formula for the length of an arc (L) in a circle is given by:
\[ L = r \theta \]
where \( r \) is the radius of the circle and \( \theta \) is the angle in radians.

### Step 2: Rearrange the formula to find the angle
To find the angle \( \theta \), we rearrange the formula:
\[ \theta = \frac{L}{r} \]
In this case, we need to convert \( \theta \) from radians to degrees.

### Step 3: Substitute the values
Given:
- Length of the arc \( L = 22 \) cm
- Radius of the circle \( r = 100 \) cm

Substituting these values into the formula:
\[ \theta = \frac{22}{100} \]

### Step 4: Calculate the angle in radians
Calculating the above expression:
\[ \theta = 0.22 \text{ radians} \]

### Step 5: Convert radians to degrees
To convert radians to degrees, we use the conversion factor:
\[ \text{Degrees} = \theta \times \frac{180}{\pi} \]
Using \( \pi \approx \frac{22}{7} \):
\[ \text{Degrees} = 0.22 \times \frac{180}{\frac{22}{7}} \]

### Step 6: Simplify the expression
Calculating the conversion:
\[ \text{Degrees} = 0.22 \times \frac{180 \times 7}{22} \]
\[ \text{Degrees} = 0.22 \times \frac{1260}{22} \]
\[ \text{Degrees} = 0.22 \times 57.27 \]
\[ \text{Degrees} \approx 12.6 \]

### Step 7: Finalize the answer
The angle in degrees can also be expressed in degrees and minutes. The decimal part \( 0.6 \) of a degree can be converted to minutes:
\[ 0.6 \times 60 = 36 \text{ minutes} \]
Thus, the final answer is:
\[ 12 \text{ degrees } 36 \text{ minutes} \]

### Final Answer:
The angle subtended at the center of the circle by the arc of length 22 cm is \( 12 \text{ degrees } 36 \text{ minutes} \).

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