Question

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

Answer 1

If m∠UNR = 180° find m∠RNS

A. 27

Answer 2

Option A) m∠RNS=27°

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=(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.