https://file.aiquickdraw.com/mathbot/file/17290455664407l8defpo.jpg

The image shows a **regular polygon** at the center of a stained glass window. To answer the questions about the interior and exterior angles, let’s proceed step-by-step.

### Step 1: Determine the number of sides (n) of the polygon.
Looking at the stained glass design, the polygon in the center has **12 sides** (a dodecagon). We can now use this value to calculate the angles.

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### Step 2: Formula for interior angle of a regular polygon
The formula to calculate the **measure of each interior angle** of a regular polygon with \(n\) sides is:

\[
\text{Interior Angle} = \frac{(n - 2) \times 180^\circ}{n}
\]

For \(n = 12\):
\[
\text{Interior Angle} = \frac{(12 - 2) \times 180^\circ}{12} = \frac{10 \times 180^\circ}{12} = \frac{1800^\circ}{12} = 150^\circ
\]

So, each interior angle of the polygon is **150°**.

---

### Step 3: Formula for exterior angle
The **exterior angle** is related to the interior angle since they are supplementary. That means:

\[
\text{Exterior Angle} = 180^\circ - \text{Interior Angle}
\]

\[
\text{Exterior Angle} = 180^\circ - 150^\circ = 30^\circ
\]

Alternatively, we can use the direct formula for exterior angles:

\[
\text{Exterior Angle} = \frac{360^\circ}{n}
\]

For \(n = 12\):
\[
\text{Exterior Angle} = \frac{360^\circ}{12} = 30^\circ
\]

So, each exterior angle is **30°**.

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### Final Answers:
- **Interior angle** of the polygon: **150°**
- **Exterior angle** of the polygon: **30°**

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Do you need further clarifications or additional details?

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### Related Questions:
1. How do interior and exterior angles change as the number of sides increases?
2. Can a polygon have exterior angles that are not equal?
3. What is the sum of all the interior angles for this 12-sided polygon?
4. How would the interior angle change for an octagon (8 sides)?
5. How do regular polygons fit together to tile a plane perfectly?

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**Tip:** The sum of all exterior angles of any regular polygon is always \(360^\circ\), no matter the number of sides!

The center of the stained glass window is in the shape of a regular polygon. What is the measure of each interior angle? What is the measure of each exterior angle?

Learn how to calculate the interior and exterior angles of a regular dodecagon using the appropriate formulas. This geometry problem is perfect for students in Grades 7-9, covering polygon angle calculations and key geometric concepts.

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