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ABCDEFGHIJK is a regular decagon. The rotation centered at G with an angle of a takes D to J. Given that a < 180 degrees, find a.

 Apr 26, 2020
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Answer: 72

 

Explanation:

ALWAYS DRAW A DIAGRAM

First find the measure of an interior angle of a decagon.

180-360/n, n=10, so it's 144 degrees.

There are trapezoids GHIJ and DEFG, where DE and FG and GH and IJ are congruent and equal the side length.

The angle HGJ is one angle of the trapezoid GHIJ, and we can find that angle is 36 degrees (remember to draw it out).

Same with angle FGD.

Therefore, angle DGJ is 144 (the interior angle) minus 36 twice, or 144-36*2=72 degrees.

a=72.

 

You are very welcome!

:P

 Apr 26, 2020

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