Each interior angle of a dodecagon will be 150

^{o}. Now, we are interested in finding the sum of angles of a dodecagon. Let us do the following construction to decide it and let us verify against the value obtained by the formula for the sum of angles in a polygon of n sides. Take any point X in the interior of the dodecagon, and join it to the vertices of the dodecagon. Then, we form twelve triangles as shown below. The triangles need not be similar, but it is known that the sum of the three angles in a triangle is always 180°.

As we have twelve triangles, the sum of the angles of the twelve triangles be 12×180°=2160°. But, the angles at the point X is not part of the sum of the angles of the dodecagon and the sum of angles at X is equal to one complete angle, 360°. Thus,

Sum of angles of a Dodecagon=2160°-360°=1800°For a polygon with n sides,

Sum of Angles= (n-2)180°

For a Dodecagon, n=12. So,

Sum of angles of a Dodecagon = (n-2) 180°

=(12-2) 180°

=10×180°

=1800°

But, in case of an irregular dodecagon, the measures of interior angles based on the lengths of sides. So, it is possible to find out the measure of each angle. In case of regular dodecagons, the measures of all interior angles are equal. As there are 12 angles in the regular dodecagon and sum of angles is 1800°. So,

An interior angle in a Regular Dodecagon= $\frac{1800^o}{12}$=150°