The interior angle between the sides of the polygon $ = \frac{(n-2) \times 180^{\circ}}{n},$ where $n = $ number of sides of the polygon.
Here, $n = 10,$ therefore the interior angle between the sides of the polygon $ = \frac{(10-2) \times 180^{\circ}}{10}$
$\qquad = 8 \times 18^{\circ} = 144^{\circ}.$
So, the correct answer is $(D).$