SOLUTION: Hi! I was wondering how you would answer this question. two rays bisect two consecutive angles of a regular decagon and intersect in the decagon's interior. Find the measure of the

Algebra ->  Polygons -> SOLUTION: Hi! I was wondering how you would answer this question. two rays bisect two consecutive angles of a regular decagon and intersect in the decagon's interior. Find the measure of the      Log On


   

Question 707864: Hi! I was wondering how you would answer this question. two rays bisect two consecutive angles of a regular decagon and intersect in the decagon's interior. Find the measure of the acute angles formed by the intersecting rays. If if is possible can you show me how you would draw this and then explain how to find this becuase I am really confused! Thanks so much:D
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First find the measure of each interior angle in the regular decagon

I = (180(n-2))/n

I = (180(10-2))/10

I = (180(8))/10

I = 1440/10

I = 144

So the measure of each interior angle of a 10-sided polygon is 144 degrees.

The rays bisect the interior angles, so they get cut in half to get 144/2 = 72 degrees

There are 2 such angles (a drawing will show you this). So if x is the remaining angle, then x+72+72 = 180 since all angles in a triangle add to 180 degrees.

Solve for x

x+72+72=180

x+144=180

x=180-144

x=36

So the rays intersect at the angle of 36 degrees. This is because the remaining angle is exactly the angle which is formed when the two rays intersect.