Find the sum of the measure of the interior angles of each polygon. \( \begin{array}{l}\text { 4. Octagon } \\ 5.15 \text {-gon }\end{array} \)

To find the sum of the measures of the interior angles of a polygon, we can use the formula: \[ S = (n - 2) \times 180 \] where \( S \) is the sum of the interior angles and \( n \) is the number of sides of the polygon. Let's calculate the sum of the interior angles for both the octagon (8 sides) and the 15-gon (15 sides). 1. **For the octagon (n = 8):** \[ S = (8 - 2) \times 180 \] 2. **For the 15-gon (n = 15):** \[ S = (15 - 2) \times 180 \] Now, let's perform the calculations. Calculate the value by following steps: - step0: Calculate: \(\left(8-2\right)\times 180\) - step1: Subtract the numbers: \(6\times 180\) - step2: Multiply the numbers: \(1080\) Calculate or simplify the expression \( (15 - 2) * 180 \). Calculate the value by following steps: - step0: Calculate: \(\left(15-2\right)\times 180\) - step1: Subtract the numbers: \(13\times 180\) - step2: Multiply the numbers: \(2340\) The calculations yield the following results: 1. For the octagon (8 sides): \[ S = (8 - 2) \times 180 = 1080 \] So, the sum of the interior angles of the octagon is \( 1080 \) degrees. 2. For the 15-gon (15 sides): \[ S = (15 - 2) \times 180 = 2340 \] Thus, the sum of the interior angles of the 15-gon is \( 2340 \) degrees. In summary: - The sum of the interior angles of the octagon is \( 1080 \) degrees. - The sum of the interior angles of the 15-gon is \( 2340 \) degrees.