A polygon is regular if all its sides and angles are the same. Find the measure of each angle in a regular dodecagon (12-sided polygon).

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![](https://cdn.mathpix.com/cropped/2024_04_17_56b7dc2d6d003fd57087g-1.jpg?height=405&width=400&top_left_y=691&top_left_x=882)

A regular dodecagon can be divided into 10 triangles, as shown above. The sum of the angles in each triangle is $180^{\circ}$, so the sum of the angles in the dodecagon is $10 \cdot 180^{\circ}=1800^{\circ}$. Since it is regular, all the angles are the same, so we divide by 12 to get $1800^{\circ} / 12=150^{\circ}$ for each angle.