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In this section, the equation to find the degree measure of an exterior angle of a regular polygon will be discovered. The use of a calculator is helpful but not necessary.

Pentagon with one side extending past each angle

In pentagon PENTA: ∠P and ∠1, form a linear pair and are supplementary.

Answer the following questions.

Interactive button. Assistance may be required. _____ ∠4 and ∠T form a linear pair and are supplementary.
∠N and Interactive button. Assistance may be required. _____ ∠3 form a linear pair and are supplementary.
An interior angle and its corresponding exterior angle add up to Interactive button. Assistance may be required. _____ 180 degrees.
When two adjacent angles form a straight line, the angles are Interactive button. Assistance may be required. _____ supplementary; a linear pair.

Triangle with one side extending past each angle, square with one side extending past each angle, pentagon with one side extending past each angle, hexagon with one side extending past each angle, octagon with one side extending psat each angle

Polygon	Number of Angles	Sum of Interior Angles (total degrees in interior angles)	Number of Degrees in Each Interior Angle	Number of Degrees in Each Exterior Angle	Sum of Exterior Angles
Triangle	Interactive button. Assistance may be required. _____ 3	Interactive button. Assistance may be required. _____ 180	Interactive button. Assistance may be required. _____ 60	Interactive button. Assistance may be required. _____ 120	Interactive button. Assistance may be required. _____ 3 x 120 = 360
Quadrilateral	Interactive button. Assistance may be required. _____ 4	Interactive button. Assistance may be required. _____ 360	Interactive button. Assistance may be required. _____ 90	Interactive button. Assistance may be required. _____ 90	Interactive button. Assistance may be required. _____ 4 x 90 = 360
Pentagon	Interactive button. Assistance may be required. _____ 5	Interactive button. Assistance may be required. _____ 540	Interactive button. Assistance may be required. _____ 108	Interactive button. Assistance may be required. _____ 72	Interactive button. Assistance may be required. _____ 5 x 72 = 360
Hexagon	Interactive button. Assistance may be required. _____ 6	Interactive button. Assistance may be required. _____ 720	Interactive button. Assistance may be required. _____ 720	Interactive button. Assistance may be required. _____ 60	Interactive button. Assistance may be required. _____ 6 x 60 = 360
Octagon	Interactive button. Assistance may be required. _____ 8	Interactive button. Assistance may be required. _____ 1080	Interactive button. Assistance may be required. _____ 135	Interactive button. Assistance may be required. _____ 45	Interactive button. Assistance may be required. _____ 8 x 45 = 360
n-gon - is a polygon with n number of sides	Interactive button. Assistance may be required. _____ n	Interactive button. Assistance may be required. _____ (n - 2)•180	Interactive button. Assistance may be required. _____ (n minus 2) times 180 over n (n − 2) × 180 n	Interactive button. Assistance may be required. _____ 180 − (n minus 2) times 180 over n (n − 2) × 180 n or 360 over n 360 n	Interactive button. Assistance may be required. _____ 360

Use the figures above to assist in completing the chart above to discover the equation for the degree or measure of an exterior angle of a regular polygon.

Answer the following questions.

To find the measure of an exterior angle of a polygon, the formula is Interactive button. Assistance may be required. _____ 180 − (n minus 2) times 180 over n (n − 2) × 180 n or 360 over n 360 n .
To find the sum of the exterior angles, Interactive button. Assistance may be required. _____ Multiply the number of sides of the polygon by the measure of one exterior angle.