Question

If m∠UNR = 180° find m∠RNS A. 27° B. 34° C. 59° D. 94°

Answer 1

Answer:

Option A) m∠RNS=27°

Step-by-step explanation:

We know that $m$∠UNR = 180°. This tells us that the Sum of the enclosed angles should equal 180°, by trigonometry. So the enclosed angles are:

$m$∠RNS = $(3x+6)^{o}$

$m$∠SNT= $(13x+3)^{o}$

$m$∠TNU= $(10x-11)^{o}$

Now let us add all the angles and solve for the value of $x$ as follow:

$m_{RSN}+m_{SNT}+m_{TNU}=m_{UNR}\\\\(3x+6)+(13x+3)+(10x-11)=180\\\\3x+13x+10x+6+3-11=180\\\\26x-2=180\\\\26x=180+2\\\\26x=182$

$x=\frac{182}{26} \\\\x=7$

Now lets plug in the value into the expression for angle $m$∠RNS to find the angle as:

$RNS = (3x+6)^{o}\\\\RNS=(3(7)+6)^{o}\\\\RNS=(21+6)^{o}\\\\RNS=27^{o}$

Thus Option A. is the correct answer.