SOLUTION: In the regular octagon below, find x. https://web2.0calc.com/api/ssl-img-proxy?src=%2Fimg%2Fupload%2Fb8a0eeb81cd61ebb5182a8a7%2Fregular-octagon2.jpg

Algebra ->  Geometry-proofs -> SOLUTION: In the regular octagon below, find x. https://web2.0calc.com/api/ssl-img-proxy?src=%2Fimg%2Fupload%2Fb8a0eeb81cd61ebb5182a8a7%2Fregular-octagon2.jpg      Log On


   



Question 1210531: In the regular octagon below, find x.
https://web2.0calc.com/api/ssl-img-proxy?src=%2Fimg%2Fupload%2Fb8a0eeb81cd61ebb5182a8a7%2Fregular-octagon2.jpg

Answer by greenestamps(13292) About Me  (Show Source):
You can put this solution on YOUR website!


The longer of the two diagonals in the figure is perpendicular to the side of the octagon, so the angle it forms with the side of the octagon in 90 degrees.

The angle measure of each interior angle of a regular octagon is 180-%28360%2F8%29=135 degrees.

The shorter of the two diagonals in the figure forms an isosceles triangle with two sides of the octagon. The measure of each acute angle in that isosceles triangle is %28180-135%29%2F2+=+22.5 degrees.

So the measure of the angle x in the figure is 90-22.5+=+67.5 degrees.

ANSWER: 67.5 degrees