Summative 7 Find the measure of each interior angle of a regular octagon. Show your work.

To find the measure of each interior angle of a **regular octagon**, follow these steps: ### Step 1: Understand the Properties of a Regular Octagon - A **regular octagon** has **8 sides**. - All sides are of equal length, and all interior angles are equal. ### Step 2: Use the Formula for the Interior Angle of a Regular Polygon The formula to find the measure of each interior angle of a regular polygon is: \[ \text{Interior Angle} = \frac{(n - 2) \times 180^\circ}{n} \] where: - \( n \) = number of sides ### Step 3: Plug in the Values For an octagon, \( n = 8 \). \[ \text{Interior Angle} = \frac{(8 - 2) \times 180^\circ}{8} \] \[ \text{Interior Angle} = \frac{6 \times 180^\circ}{8} \] ### Step 4: Perform the Calculation \[ \text{Interior Angle} = \frac{1080^\circ}{8} = 135^\circ \] ### Conclusion Each interior angle of a **regular octagon** measures **135 degrees**.