Question

find the measure of each exterior angle of a regular polygon of
i 8 sides

Answer 1

$\textbf{Solution:}$
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♦ As we all know that sum of Exterior angles of polygon is 360°

♦Since it has 8 sides , so it is an octagon.

♦ As, it is a regular octagon, so each of the interior angles of octagon are equal.

Now,

$= > \frac{(n - 2) \times 180}{n} \\ \\ = > \frac{(8 - 2) \times 180}{8} \\ \\ = > \frac{6 \times 180}{8} \\ \\ = > \frac{1080}{8} \\ \\ = > 135 \: \: degree$
♦ This means that each interior angle of the regular octagon is equal to $\textbf{135}$ degrees.

♦ Each exterior angle is the supplementary angle to the interior angle at the vertex of the polygon.

•°• Each exterior angle = (180 - 135) = 45°.

Therefore, each exterior angle of a regular polygon with 8 sides is $\textbf{45 degree}$ .
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$\textbf{Thank you!!}$

Answer 2

Answer:

45°

Step-by-step explanation:

     1. (n-2) x 180°      

               n°

     2. = (8-2) x 180°

                     8

    3.  = 6 x 180°

                 8

     4.  = 1080°

                8

     5.  = 135°

     

     6. Each exterior angle is supplementary, so (180° - 135°) = 45°

    7. ∴ Each exterior angle is 45°.