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

Ask by Smith Barnett. in the United States
Feb 27,2025

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The sum of the interior angles of an octagon is 1080 degrees, and the sum of the interior angles of a 15-gon is 2340 degrees.

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To find the sum of the measure of the interior angles of a polygon, you can use the formula: \[ \text{Sum of interior angles} = (n - 2) \times 180^\circ \] where \(n\) is the number of sides. For the octagon (8 sides): \[ \text{Sum of interior angles} = (8 - 2) \times 180^\circ = 6 \times 180^\circ = 1080^\circ \] For the 15-gon (15 sides): \[ \text{Sum of interior angles} = (15 - 2) \times 180^\circ = 13 \times 180^\circ = 2340^\circ \] So, the sum of the measures of the interior angles of an octagon is \(1080^\circ\) and that of a 15-gon is \(2340^\circ\).

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