Find the measure of one interior angel if a regular 23-gona. 164.3°b. 165.6°c. 160°d. 161.1°

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°

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The 23 exterior angles add to 360. The interior angles are supplements of the exterior angles.

180 - 360/23 = 3780 / 23 = 164.3478...

a

24

step-by-step explanation: