To find the number of sides \( n \) of a polygon given the measure of an interior angle, we can use the formula for the measure of an interior angle of a regular polygon:
\[ \text{Interior Angle} = \frac{(n - 2) \times 180°}{n} \]
We can rearrange this formula to solve for \( n \):
\[ \text{Interior Angle} \times n = (n - 2) \times 180° \]
\[ \text{Interior Angle} \times n = 180n - 360 \]
\[ 180n - \text{Interior Angle} \times n = 360 \]
\[ n(180 - \text{Interior Angle}) = 360 \]
\[ n = \frac{360}{180 - \text{Interior Angle}} \]
Now we'll apply this formula for both angles:
- For an interior angle of 160°:
\[ n = \frac{360}{180 - 160} = \frac{360}{20} = 18 \]
- For an interior angle of 156°:
\[ n = \frac{360}{180 - 156} = \frac{360}{24} = 15 \]
Therefore:
- For an interior angle of 160°, \( n = 18 \).
- For an interior angle of 156°, \( n = 15 \).