Search 72,101 tutors
FIND TUTORS
Ask a question
0 0

Need to find the measure of one interior angle in a regular 11-gon.

Tutors, please sign in to answer this question.

2 Answers

The sum of all the interior angles of a regular polygon can be found with the equation (n-2) × 180°.  "n" in this equation refers to the number of sides in the polygon.  (We can recall this equation easily if we remember that regular polygons can be divided up into triangles, and that the sum of angle triangles interior angles must equal 180°)

 

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

 

Regular polygons are regular because they are equiangular (all angles of polygon are congruent) and equilateral (all sides of polygon are congruent).  So if we know that the 11-gon polygon has 11 equal interior angles, we can divide the total sum of the interior angles by "n" to determine the measure of one interior angle.

 

[(n-2) × 180°] ÷ n = measure of one interior angle

[(11-2) × 180°] ÷ 11 = 1620° ÷ 11 = 147.27°

The sum of the angles of any polygon is (n-2)*180, where n = number of sides. Therefore, for a regular polygon we would divide the result by n to find the measure of one interior angle: [(n-2)*180]/n I'll leave the calculations to the student.