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VMariaS [17]
2 years ago
9

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.

Mathematics
2 answers:
inna [77]2 years ago
8 0

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°


german2 years ago
5 0

Answer:

<em>The measure of \angle KNL = 87\°</em>

Step-by-step explanation:

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

So,  \angle JNM = \angle KNL  <em>(As they are vertical angles)</em>

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

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

That means.......

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

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

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