Quiz
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Interior Angle: 135^(∘)
Exterior Angle: 45^(∘)
The stop sign has eight sides and we know that it is a regular polygon. Therefore, it is an octagon.
( 8-2)* 180^(∘)=6* 180^(∘)= 1080^(∘) Now we will find the measure of each interior angle. A regular n-gon has n congruent angles. Thus to find the measure of one interior angle of the stop sign, we need to divide the sum of measures of all interior angles, 1080^(∘), by the number of sides, 8. 1080^(∘)/8=135^(∘) The measure of each interior angle of the stop sign is 135^(∘).
By the Polygon Exterior Angles Theorem the sum of the measures of the exterior angles of a convex polygon is 360^(∘). A regular n-gon has n congruent exterior angles. Thus to find the measure of one exterior angle of the stop sign we will divide the sum of all exterior angles, 360^(∘), by the number of sides, 8. 360^(∘)/8=45^(∘) The measure of each exterior angle of the stop sign is 45^(∘).