SOLUTION: i need help on proprties and area of quadrilaterals; my question is how to find the measure of an interior angle and exterior angle of any regular nonagon

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Begin by constructing the nonagon. To do this we pick a center point from which we draw nine radiating lines. Each of the radiating lines must be straight and of equal length. Also, the angle between any pair of adjacent radiating lines must be equal to the angle between every other pair of adjacent radiating lines. This will form a star-like pattern. The sum of the angles formed by adjacent lines is 360 degrees, so each of these angles must be degrees

Pick two adjacent radiating lines and call them l₁ and l₂. The endpoints of l₁ are C (the center) and E₁ and the endpoints of l₂ are C (the center) and E₂. If we draw a line from E₁ to E₂, we form a triangle CE₁E₂. If we repeat this process for every pair of adjacent lines, the lines E₁E₂, E₂E₃, E₃E₄, E₄E₅, E₅E₆, E₆E₇, E₇E₈, E₈E₉ and E₉E₁form a regular nonagon. Moreover, the nonagon is formed from similar isoceles triangles.

We know that the angle E_iCE_j = 40 degrees, where i and j are the end points of two adjacent radiating lines. Given that the sum of the interior angles of a triangle = 180 and the angle CE_iE_j equals the angle CE_jE_i we conclude that CE_iE_j = CE_jE_i = .

Now, consider the point E₁. This is a vertex on the nonagon, the triangle CE₁E₂ and the triangle CE₉E₁. The interior angle of the nonagon at this point is E₉E₁E₂. This angle is formed by adding the angles CE₁E₂ and CE₁E₉. We just deteremined that each of these angles is 70 degrees, so the interior angle formed by E₉E₁E₂ is 140 degrees.

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A exterior angle is the supplementary angle to the interior angle. That is, the sum of the exterior and interior angle is 180 degrees. To find the exterior angle, we compute 180 less the interior angle or degrees.