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
Where is the sum of the interior angles
and 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 =
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
∴
From the formula
Measure of one interior angle in a regular polygon =
Measure of one interior angle in the regular 23-gon =
=
=
= 164.3478°
≅ 164.3°
Hence, the measure of one interior angle of a regular 23-gon is 164.3°