Question

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.

Answer 1

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°

Answer 2

Answer:

The measure of $\angle KNL = 87\°$

Step-by-step explanation:

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

So,  $\angle JNM = \angle KNL$  (As they are vertical angles)

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