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Bunuel

The figure below is a regular octagon. What is the combined measure of all of the indicated angles?

(A) 720°
(B) 960°
(C) 1,080°
(D) 1,220°
(E) 1,440°


Attachment:
2020-12-30_20-51-07.png

Marked angles are interior angles.

Interior Angles of a polygon \(= 180(n-2); \ n\) is the number of sides.
There 8 sides of an octagon.

Thus, \(180(8-2)=180*6=1080\)

The answer is \(C\)
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Bunuel

The figure below is a regular octagon. What is the combined measure of all of the indicated angles?

(A) 720°
(B) 960°
(C) 1,080°
(D) 1,220°
(E) 1,440°


Attachment:
2020-12-30_20-51-07.png
Solution:

Recall that the sum of the measures of all the angles of a n-sided polygon (regardless if it's regular or not) is 180(n - 2) degrees. Since here we have an octagon, which is an 8-sided polygon, the sum of the measures of all the angles is therefore 180(8 - 2) = 180 x 6 = 1080 degrees.

Alternate Solution:

We can also use the fact that the sum of exterior angles of any polygon is 360 degrees. Since an octagon has eight exterior angles and since we have a regular octagon, each exterior angle is 360/8 = 45 degrees. Thus, each interior angle measures 180 - 45 = 135 degrees, and the sum of the interior angles is 135 x 8 = 1080 degrees.

Answer: C
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