Question 707864
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.