A regular nonagon is 9-sided polygon with all congruent interior angles and congruent sides. If all interior angles are congruent, then all exterior angles are congruent too.
The sum of the measures of exterior angles of an arbitrary n-sided polygon is equal to 360°. Therefore, the measure of exterior angle of regular nonagon is:
[tex]\dfrac{360^{\circ}}{9}=40^{\circ}.[/tex]
Then the measure of each interior angle of regular nonagon is equal to
[tex]180^{\circ}-40^{\circ}=140^{\circ}.[/tex]
Answer: the measure of each interior angle is [tex]140^{\circ},[/tex] the measure of each exterior angle is [tex]40^{\circ}.[/tex]
Measure of each interior angle of a regular nonagon = [tex]140^0[/tex]
Measure of each exterior angle of a regular nonagon = 40°
Number of sides of a nonagon = 9
Measure of each interior angle of a regular polygon is [tex]\frac{180(n-2)}{n}[/tex]
Measure of each exterior angle of a regular polygon is [tex]\frac{360}{n}[/tex]
A nonagon is a polygon with 9 sides
Substitute n = 9 into the formula for each interior angle of a regular polygon to get the measure of each interior angle of a regular nonagon
Measure of each interior angle of a regular nonagon = [tex]\frac{180(9-2)}{9}[/tex]
Measure of each interior angle of a regular nonagon = [tex]\frac{180(7)}{9}[/tex]
Measure of each interior angle of a regular nonagon = [tex]140^0[/tex]
Measure of each exterior angle of a regular nonagon = [tex]\frac{360}{9}[/tex]
Measure of each exterior angle of a regular nonagon = 40°
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