Answer:
Option A) m∠RNS=27°
Step-by-step explanation:
We know that [tex]m[/tex]∠UNR = 180°. This tells us that the Sum of the enclosed angles should equal 180°, by trigonometry. So the enclosed angles are:
[tex]m[/tex]∠RNS = [tex](3x+6)^{o}[/tex]
[tex]m[/tex]∠SNT= [tex](13x+3)^{o}[/tex]
[tex]m[/tex]∠TNU= [tex](10x-11)^{o}[/tex]
Now let us add all the angles and solve for the value of [tex]x[/tex] as follow:
[tex]m_{RSN}+m_{SNT}+m_{TNU}=m_{UNR}\\\\(3x+6)+(13x+3)+(10x-11)=180\\\\3x+13x+10x+6+3-11=180\\\\26x-2=180\\\\26x=180+2\\\\26x=182\\\\[/tex]
[tex]x=\frac{182}{26} \\\\x=7[/tex]
Now lets plug in the value into the expression for angle [tex]m[/tex]∠RNS to find the angle as:
[tex]RNS = (3x+6)^{o}\\\\RNS=(3(7)+6)^{o}\\\\RNS=(21+6)^{o}\\\\RNS=27^{o}[/tex]
Thus Option A. is the correct answer.
