The sum of the angles of any kind of polygon is (n-2)*180, wherein n = variety of sides. Therefore, for a continuous polygon we would certainly divide the result by n to uncover the measure of one interior angle: <(n-2)*180>/n I"ll leave the calculations to the student.

You are watching: Find the measure of one interior angle

The amount of all the internal angles of a constant polygon have the right to be found with the equation (n-2) × 180°. "n" in this equation describes the variety of sides in the polygon. (We have the right to recall this equation easily if us remember that constant polygons have the right to be divided up right into triangles, and also that the amount of edge triangles inner angles have to equal 180°)

So, the amount of all interior angles in our continual 11-gon polygon = (11-2)× 180°= 1620°

Regular polygons are regular since they are**equiangular** (all angle of polygon are congruent) and **equilateral**(all political parties of polygon are congruent). So if we recognize that the 11-gon polygon has actually 11 equal internal angles, we deserve to divide the total sum the the inner angles by "n" to identify the measure of one inner angle.

<(n-2)× 180°> ÷n = measure of one inner angle

<(11-2)× 180°> ÷ 11 =1620°÷ 11 = **147.27°**

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