What is the ratio of the angles of the triangle inscribed in a regular octagon?

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What is the ratio of the angles of the triangle inscribed in a regular octagon?

Required ratio = 67.5 : 45 = 3 : 2.

What is the approximate area of a regular octagon?

Thus, the base of the triangle is a, which is the length of the side of the polygon and OD is the height of the triangle. Area of the octagon is given as 8 x Area of Triangle. A = 4 sin ⁡ π 4 R 2 = 2 2 R 2 ≃ 2.828 R 2 .

How do you find the side length of a regular octagon?

Multiply the diameter’s length, the distance from vertex to opposite vertex, by 0.383 to calculate a side’s length. For example, the diameter is 10 inches — 10 inches multiplied by 0.383 results in 3.83 inches.

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What is the area of regular octagon inscribed in a circle of radius r?

So, the correct answer is “ =2√2r2 ”.

How many times can a regular octagon be rotated?

Symmetry in regular octagons A regular octagon has 8 lines of symmetry and a rotational symmetry of order 8. This means that it can be rotated in such a way that it will look the same as the original shape 8 times in 360°.

How do you find the area of a regular octagon with an apothem?

You will obtain the total area of the octagon: area of octagon = 8 * base * height / 2 = perimeter * apothem / 2 .

How do you find the center of an octagon?

To find the measure of the central angle of a regular octagon, make a circle in the middle… A circle is 360 degrees around… Divide that by eight angles… So, the measure of the central angle of a regular octagon is 45 degrees.

What is the shape of the Octagon labeled abcdefgh?

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Now your octagon is labeled ABCDEFGH. Angle ABC is one of the interior angles so angle ABC equals 135 degrees. Angle ACD = 112.5 degrees as shown in the following picture. As you can see, Angle ACD creates a small triangle ABC. Since this is a regular polygon, then triangle ABC is an isosceles triangle.

What is the angle ACD of an octagon?

In an octagon, n = 8, and each interior angle would be 6*180/8 = 1080/8 = 135 degrees. Now your octagon is labeled ABCDEFGH. Angle ABC is one of the interior angles so angle ABC equals 135 degrees. Angle ACD = 112.5 degrees as shown in the following picture.

What is the value of angle ACD for 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 22.5 degrees, then angle ACD is equal to 135 minus 22.5 = 112.5 degrees.

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How do you find the interior angles of abcabcdefgh?

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 = ((n-2)*180)/n where i = each interior angle and n = number of sides. In a triangle, n = 3, and each interior angle would be 1*180/3 = 60 degrees.