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The questions from the image ask about finding the number of sides in a regular polygon given the measure of an interior angle. 

### Formula:
For a regular polygon, the measure of an interior angle \( A \) is given by the formula:
\[
A = \frac{(n-2) \times 180^\circ}{n}
\]
where \( n \) is the number of sides of the polygon.

We can rearrange this to solve for \( n \):
\[
n = \frac{360^\circ}{180^\circ - A}
\]

Let's solve for each question:

### Question 2: Interior angle is \( 150^\circ \)
\[
n = \frac{360^\circ}{180^\circ - 150^\circ} = \frac{360^\circ}{30^\circ} = 12
\]
So, the polygon has **12 sides**.

### Question 3: Interior angle is \( 170^\circ \)
\[
n = \frac{360^\circ}{180^\circ - 170^\circ} = \frac{360^\circ}{10^\circ} = 36
\]
So, the polygon has **36 sides**.

Would you like more details or have any questions?

### Related Questions:
1. How do you find the sum of interior angles of a polygon?
2. What is the formula for the exterior angle of a regular polygon?
3. How many sides does a polygon have if its interior angle is \(160^\circ\)?
4. What is the relationship between the interior and exterior angles of a regular polygon?
5. How do you calculate the number of diagonals in a polygon?

### Tip:
The exterior angle of a regular polygon is simply \( 360^\circ / n \), and the sum of exterior angles of any polygon is always \( 360^\circ \), no matter how many sides it has.

2. The measure of an interior angle of a regular polygon is 150°. How many sides does the polygon have? 3. The measure of an interior angle of a regular polygon is 170°. How many sides does the polygon have?

Learn how to determine the number of sides of a regular polygon given the measure of its interior angles (150° and 170°). This geometry problem involves the formula for interior angles and is suitable for students in Grades 8-10.

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