The sum of all Internal angles of a regular polygon whose one external angle is `20^@` is

Options

A. `6400^@`
B. `3200^@`
C. `2880^@`
D. `1440^@`

Answer

To find the sum of all internal angles of a regular polygon whose one external angle is \(20^\circ\), we can follow these steps:

### Step 1: Determine the number of sides (n) of the polygon
The formula to find the number of sides of a polygon based on its external angle is:
\[ n = \frac{360^\circ}{\text{external angle}} \]
Given that the external angle is \(20^\circ\):
\[ n = \frac{360^\circ}{20^\circ} = 18 \]

### Step 2: Use the formula for the sum of internal angles
The formula to calculate the sum of internal angles of a polygon is:
\[ \text{Sum of internal angles} = (n - 2) \times 180^\circ \]
Substituting \(n = 18\) into the formula:
\[ \text{Sum of internal angles} = (18 - 2) \times 180^\circ = 16 \times 180^\circ \]

### Step 3: Calculate the sum
Now, we perform the multiplication:
\[ 16 \times 180^\circ = 2880^\circ \]

### Final Answer
The sum of all internal angles of the polygon is \(2880^\circ\).

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