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I need help with polygons

 

Let B, A, and D be three consecutive vertices of a regular -gon.  A regular heptagon is constructed on AB with a vertex C next to A  Find  angle BCD in degrees.

 May 2, 2023
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Angle BCD is equal to 65.5°.

Step-by-step explanation:

What is the formula for the interior angle of a regular polygon?

The interior angle of a polygon = sum of interior angles and the number of sides is the formula for determining the amount of an interior angle.

It is given that B, A, and D are three consecutive vertices of a regular 8-gon.

The interior angle of a regular 8-gon (Octagon) is 135°.

It is given that C is a vertex of a regular heptagon(7-gon) whose one side is AB.

C, B, and D are at equal distances from A.

So A is the center and C, B, and D are points on the circle.

BD is the cord that is making an angle of 135° at A(center).

At the circumference, the cord makes half the angle.

So angle BCD is equal to 135/2 = 65.5°.

 May 3, 2023

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