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The problem presented asks about a regular polygon with 12 sides.

### Part (a): What is the outer angle of this regular polygon?

For a regular polygon, the formula for the exterior (outer) angle is:

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

Where \(n\) is the number of sides. In this case, \(n = 12\):

\[
\text{Exterior angle} = \frac{360^\circ}{12} = 30^\circ
\]

So, the outer angle of this regular polygon is **30°**.

### Part (b): What is the measure of an inner angle?

The interior (inner) angle of a regular polygon can be found using the formula:

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

From part (a), we know the exterior angle is \(30^\circ\):

\[
\text{Interior angle} = 180^\circ - 30^\circ = 150^\circ
\]

So, the inner angle is **150°**.

### Summary:
- (a) The outer angle of the regular polygon is **30°**.
- (b) The inner angle is **150°**.

Would you like more details on the formulas or a deeper explanation? Here are five related questions to consider:

1. What is the sum of all the exterior angles of any polygon, and why is it always the same?
2. How do you calculate the sum of the interior angles of a polygon?
3. How does the number of sides in a polygon affect the size of the exterior angle?
4. Can a polygon have an exterior angle larger than 90°?
5. What is the relationship between the interior and exterior angles of a polygon?

**Tip:** For any regular polygon, the interior and exterior angles are always supplementary (they add up to \(180^\circ\)).

The number of sides of a regular polygon is 12.
(a) What is the outer angle of this regular polygon? (30°, 60°, 120°, 150°)
(b) What is the measure of an inner angle?

Learn how to calculate the exterior and interior angles of a regular polygon with 12 sides. This geometry problem covers key concepts including polygon angle formulas. Suitable for students in Grades 6-8.

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