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Let Y, X, and W be three consecutive vertices of a regular 18-gon. A regular heptagon is constructed on Line XY,  with a vertex Z next to X. Find angle YZW, in degrees.

 Jul 30, 2020
 #1
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+1

I solved this using coordinates:

 

X = (1,0)

Y = (0.924328, 0.471208)

Z = (1.222783, -1.147542)

W = (0.924328, -0.471208)

 

==> angle BCD = 75 degrees

 Jul 30, 2020
 #3
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18-gon interior angles are 120º

 

Heptagon interior angles are 128.5714286º

 

Side lengths of both polygons are 1 unit.

 

Coordinates of Y, X, W, and Z

 

Y ( 0,0 )

X ( 1,0 )

W (1.93969262, 0.342020143)

Z (1.623489802, -0.781831482) 

 

Angle YZW = 80º  smiley

Dragan  Jul 31, 2020
edited by Dragan  Jul 31, 2020
 #2
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Let Y, X, and W be three consecutive vertices of a regular 18-gon. A regular heptagon is constructed on Line XY,  with a vertex Z next to X. Find angle YZW, in degrees.

 

Angle YZW = 80 degrees  laugh

 Jul 31, 2020

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