To find the measure of one interior angle of a regular polygon (in this case, a 10-sided equilateral polygon, known as a decagon), you can use the formula for the measure of an interior angle:
\[ \text{Interior Angle} = \frac{(n - 2) \times 180}{n} \]
where \( n \) is the number of sides in the polygon.
For a decagon, \( n = 10 \):
\[ \text{Interior Angle} = \frac{(10 - 2) \times 180}{10} \] \[ = \frac{8 \times 180}{10} \] \[ = \frac{1440}{10} \] \[ = 144 \text{ degrees} \]
So the measure of one interior angle of a regular decagon is \( 144 \) degrees.
Thus, the correct answer is A. 144 degrees.