If every interior angle of regular octagon is `135^@`, then find the external angle of it.

Options

A. `65^@`
B. `75^@`
C. `45^@`
D. `55^@`

Answer

To find the external angle of a regular octagon given that each interior angle is \(135^\circ\), we can follow these steps:

### Step 1: Understand the relationship between interior and exterior angles.
The interior and exterior angles of a polygon are supplementary, which means they add up to \(180^\circ\).

### Step 2: Use the formula to find the external angle.
Since the interior angle is given as \(135^\circ\), we can find the external angle using the formula:

\[ \text{External Angle} = 180^\circ - \text{Interior Angle} \]

### Step 3: Substitute the value of the interior angle.
Now, substituting the value of the interior angle into the equation:

\[ \text{External Angle} = 180^\circ - 135^\circ \]

### Step 4: Perform the calculation.
Now, perform the subtraction:

\[ \text{External Angle} = 45^\circ \]

### Conclusion:
Thus, the external angle of the regular octagon is \(45^\circ\).

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