What is m∠KNL? Enter your answer in the box. ° A horizontal line segment M K intersects with line segment J L at their midpoint N. The upward-left and downward-right angles formed by these lines are obtuse. The upward-left obtuse angle is labeled left parenthesis 5 x plus 2 right parenthesis degrees. The downward-right acute angle is labeled left square bracket 3 left parenthesis x plus 14 right parenthesis right square bracket degrees.

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Sicista Sicista · Answer 1 · 2018-10-18T12:46:46+02:00

Answer:

The measure of [tex]\angle KNL = 87\°[/tex]

Step-by-step explanation:

According to the below diagram, horizontal line segment [tex]MK[/tex] intersects with [tex]JL[/tex] at their midpoint [tex]N[/tex].

So, [tex]\angle JNM = \angle KNL[/tex] (As they are vertical angles)

Given that, [tex]\angle JNM = (5x+2)\°[/tex] and [tex]\angle MNL = [3(x+14)]\°[/tex]

As they are adjacent angles and points [tex]J, N[/tex] and [tex]L[/tex] are co-linear, so [tex]\angle JNM +\angle MNL = 180\°[/tex]

That means.......

[tex](5x+2)+3(x+14)=180\\ \\ 5x+2+3x+42=180\\ \\ 8x+44=180\\ \\ 8x=180-44=136\\ \\ x=\frac{136}{8}=17[/tex]

Thus, [tex]\angle KNL =\angle JNM= (5*17+2)\° = 87\°[/tex]

Аноним Аноним · Answer 2 · 2018-10-18T14:00:09+02:00

t N.

In the figure shown below

Answer:

A horizontal line segment M K intersects with line segment J L at their midpoint N.

∠J N M =(5x+2)°

∠ LN M=3( x+ 14)°

So, ∠J N M + ∠ LN M =180°[ These two angles form linear pair.Angles forming linear pair are supplementary.]

⇒5 x+ 2+ 3 (x+ 14) =180 [ By Substitution]

⇒ 5 x+2 +3 x+42°= 180°

⇒ 8 x=180°-44°

⇒8 x= 136°

⇒x= 136°÷8

⇒x=17°

So, ∠J N M =5×17 +2=87°

∠ LN M= 3×(17 +14)=3×31=93

∠J N M =∠K N L [Vertically opposite angles]

∠K N L=87°