Angles in Polygons RS and ST are 2 sides of a regular 12-sided polygon. RT is a diagonal of the polygon. Work out the size of angle STR. You must show your working.

## Step 1: First, we need to understand that a regular 12-sided polygon is a dodecagon. In a regular dodecagon, all sides and angles are equal. ## Step 2:We need to find the measure of each interior angle in the dodecagon. The formula to find the measure of each interior angle in a regular polygon is given by:### \( \textbf{Interior Angle} = \frac{(n-2) \times 180}{n} \)where is the number of sides. ## Step 3:Substitute into the formula:### \( \textbf{Interior Angle} = \frac{(12-2) \times 180}{12} = 150 \) degreesSo, each interior angle in the dodecagon is 150 degrees.## Step 4:In a regular polygon, the vertices are equally spaced around the center of the polygon. Therefore, the angle is equal to the interior angle of the dodecagon.