3 The measure of an interior angle of a regular polygon is given. Find the number of sides in the polygon. \( \begin{array}{lll}26.60 & \text { 27. } 90 & \text { 28. } 120\end{array} \)

To find the number of sides \( n \) in a regular polygon given the measure of an interior angle \( A \), you can use the formula: \[ A = \frac{(n - 2) \times 180}{n} \] Rearranging this formula allows you to solve for \( n \): \[ n = \frac{360}{180 - A} \] Now, let's apply this formula to each angle: 1. For \( A = 26.60^\circ \): \[ n = \frac{360}{180 - 26.60} = \frac{360}{153.40} \approx 2.34 \quad (\text{not a valid polygon}) \] 2. For \( A = 27.90^\circ \): \[ n = \frac{360}{180 - 27.90} = \frac{360}{152.10} \approx 2.37 \quad (\text{not a valid polygon}) \] 3. For \( A = 28.00^\circ \): \[ n = \frac{360}{180 - 28} = \frac{360}{152} \approx 2.37 \quad (\text{not a valid polygon}) \] 4. For \( A = 120^\circ \): \[ n = \frac{360}{180 - 120} = \frac{360}{60} = 6 \quad (\text{valid hexagon}) \] The only valid interior angle corresponds to a polygon with 6 sides, which is a hexagon! Fun fact: hexagons are not just beautiful shapes; they also appear in nature, like honeycomb structures!