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.