The sum of the measures of the interior angles of the decagon is 1440°
The measure of each interior angle of the decagon is 144°
The measure of each exterior angle of the decagon is 36°
The sum of the measures of the exterior angles of the decagon is 360°
Step-by-step explanation:
The rule of the sum of the measures of the interior angles of a polygon is (n - 2) × 180°, where n is the number of its sideIf the polygon is regular, then its sides are equal in length and its angles are equal in measures, then the measure of each interior angle is Â
The interior angle and the exterior angle at a vertex of a polygon formed a pair of linear angles, which means the sum of their measures is 180°
∵ The decagon is a polygon with 10 sides
∴ n = 10
→ Use the first rule above to find the sum of the measures of its
 interior angles
∵ The sum of the measures of the interior angles = (10 - 2) × 180°
∴ The sum of the measures of the interior angles = 8 × 180°
∴ The sum of the measures of the interior angles = 1440°
∵ The decagon is regular
→ Use the 2nd rule above
∴ The measure of each interior angle = 
∴ The measure of each interior angle = 144°
→ Use the 3rd rule above
∵ Measure of interior angle + measure of exterior = 180°
∵ The measure of the interior angle = 144°
∴ 144° + measure of exterior angle = 180°
→ Subtract 144 from both sides
∴ The measure of the exterior angle = 180° - 144°
∴ The measure of the exterior angle = 36°
∵ The number of the exterior angles of the decagon is 10
∵ The measure of each exterior angle is 36°
→ Multiply the number of the sides by the measure of each angle
∴ The sum of the measures of the exterior angles = 36° × 10
∴ The sum of the measures of the exterior angles = 360°
