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Kay [80]
2 years ago
11

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

Mathematics
1 answer:
LenaWriter [7]2 years ago
7 0

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.

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