The problem states that a decagon is regular. We are asked to find the measure of each interior angle of a regular decagon.

1. Problem Description

The problem states that a decagon is regular. We are asked to find the measure of each interior angle of a regular decagon.

2. Solution Steps

A decagon has 10 sides. Since the decagon is regular, all its sides are of equal length and all its interior angles are equal.

The formula for the sum of the interior angles of a polygon with $n$ sides is given by:

$$(n - 2) \times 180^{\circ}$$

In this case, $n = 10$ (since it is a decagon). Therefore, the sum of the interior angles of the decagon is:

$$(10 - 2) \times 180^{\circ} = 8 \times 180^{\circ} = 1440^{\circ}$$

Since the decagon is regular, all 10 interior angles are equal. Therefore, the measure of each interior angle is the sum of the interior angles divided by the number of sides (which is 10).

$$\text{Each interior angle} = \frac{1440^{\circ}}{10} = 144^{\circ}$$

3. Final Answer

$144^{\circ}$