Abcdefgh Is A Regular Octagon

Found 2 solutions by Alan3354, Theo:

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Answer by Alan3354(68962) (Show Source):

You can put this solution on YOUR website!
ABCDEFGH is a regular octagon summate ABC ACD ABD angles
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Each interior angle is 135 degs
ABC = 135 degs
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ACB = (180 - 135)/two = 22.5 degs, so ACD = 135 - 22.5
ACD = 112.5 degs
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ABD = ACD = 112.five degs

Answer past Theo(12311) (Show Source):

You can put this solution on YOUR website!
ABCDEFGH is a regular octagon.

If so, then each interior angle is the same.

Each angle of an octagon can be found using the following general formula:

i = ((due north-2)*180)/n where i = each interior bending and n = number of sides.

In a triangle, n = 3, and each interior angle would be ane*180/iii = sixty degrees.

In a rectangle, n = 4, and each interior angle would exist 2*180/4 = xc degrees.

In an octagon, due north = eight, and each interior angle would be 6*180/8 = 1080/8 = 135 degrees.

At present your octagon is labeled ABCDEFGH.

You lot want to observe the measure of:

ABC
ACD
ABD

Angle ABC is one of the interior angles and so angle ABC equals 135 degrees.

A moving picture of bending ABC is shown below:

Angle ACD = 112.five degrees as shown in the following picture show.

As you can see, Bending ACD creates a small triangle ABC. Since this is a regular polygon, then triangle ABC is an isosceles triangle. Since angle ABC is 135 degrees, the other 2 angles of the triangle have to be (180-135)/2 which equals 22.5 degrees. Since angle BCD is also equal to 135 degrees, and angle BCA is equal to 22.five degrees, then bending ACD is equal to 135 minus 22.5 = 112.five degrees.

Angle ABD = 112.five degrees as shown in the following moving picture.

As y'all tin can see, Angle ABD creates a modest triangle BCD. Since this is a regular polygon, so triangle BCD is an isosceles triangle. Since bending BCD is 135 degrees, the other 2 angles of the triangle have to exist (180-135)/2 which equals 22.v degrees. Since angle ABC is likewise equal to 135 degrees, and angle CBD is equal to 22.5 degrees, then angle ABD is equal to 135 minus 22.v = 112.5 degrees.

Abcdefgh Is A Regular Octagon,

Source: https://www.algebra.com/algebra/homework/Circles/Circles.faq.question.280329.html

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