The measure of one interior angle of a regular 23-gon is 164.3°
The sum of interior angles in a polygon is given by the formula
[tex]S = (n-2)180^{o}[/tex]
Where [tex]S[/tex] is the sum of the interior angles
and [tex]n[/tex] is the number of sides
To find the measure of one interior angle in a regular polygon, we divide the sum of the interior angles by the number of sides. That is,
Measure of one interior angle in a regular polygon = [tex]\frac{(n-2)180^{o} }{n}[/tex]
From the question, we are to determine the value of one interior angle of a regular 23-gon.
A regular 23-gon has 23 sides
∴ [tex]n = 23[/tex]
From the formula
Measure of one interior angle in a regular polygon = [tex]\frac{(n-2)180^{o} }{n}[/tex]
Measure of one interior angle in the regular 23-gon = [tex]\frac{(23-2)180^{o} }{23}[/tex]
= [tex]\frac{(21)180^{o} }{23}[/tex]
= [tex]\frac{3780^{o} }{23}[/tex]
= 164.3478°
≅ 164.3°
Hence, the measure of one interior angle of a regular 23-gon is 164.3°
Learn more here: https://brainly.com/question/21040657
