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# A regular octagon has 8 congruent interior angles. What is the measure of each angle?

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A regular octagon has 8 congruent interior angles. What is the measure of each angle?

Guest May 19, 2015

#2
+5453
+19

The formula for finding the sum of a polygon's interior angles is 180(n-2), where n is the number of sides/angles.

Thus, for an octagon:

Sum of interior angles = 180(8-2)

= 180(6)

= 1080

Since the 8 angles are congruent, simply divide 1080 by 8 for the measure of each angle:

1080/8 = 135 degrees

kitty<3  May 19, 2015
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#1
+81014
+10

360 / 8 = 45°   for each central angle.....the other two angles of each congruent triangle are 67.5° each

CPhill  May 19, 2015
#2
+5453
+19

The formula for finding the sum of a polygon's interior angles is 180(n-2), where n is the number of sides/angles.

Thus, for an octagon:

Sum of interior angles = 180(8-2)

= 180(6)

= 1080

Since the 8 angles are congruent, simply divide 1080 by 8 for the measure of each angle:

1080/8 = 135 degrees

kitty<3  May 19, 2015
#3
+91451
0

Kitty has done it via formula.  There is nothing wrong with that.  Thanks Kitty.

CPhill hse done it very logically, he just forgot to mention that 2 of his isoscles triangle 'leg' angles adds up to one internal ocatgon angels.  His answer is the same as Kitty's.

I really like how you did that Chris.

Melody  May 19, 2015

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