We are told that N is the incenter of the triangle. This means that it is the point of concurrency of the angle bisectors.
According to the Incenter Theorem, the incenter of a triangle is equidistant from its sides. Therefore, NQ, NR, and NS have equal lengths.
NQ=NR=NS
Since we are given the expression for the lengths of NQ and NR, we can equate them to solve for x.
Finally, we can calculate the lengths of any of the segments by substituting the value of x into either of the given expressions.
NQ: 2( 5)+1 =11
NR: 4( 5)-9 =11
Because both of these segments have a length of 11, we know NS does as well.
