Respuesta :

MrRamon
Angle KLN is congruent to angle JNM because they are vertical angles and vertical angles are congruent.
Set up am equation to make them equal to each other.
5x+2 = 3(x+14)
Distribute 3 to the values in the parentheses
5x+2 = 3x+42
Subtract 3x from both sides
2x +2 = 42
Subtract 2 from both sides
2x = 40
Divide both sides by 2
X=20

Substitute 20 for x in the angle KLN
3(20+14)
Simplify parenthesis
3(34)
Multiply
KLN =102 degrees
MrRoyal

There are several relationships between angles in a transversal.

The measure of KNL is 102 degrees.

From the figure,

Angles KNJ and JNM are corresponding angles

So, we have:

[tex]KNJ = JNM[/tex]

This gives

[tex]3(x + 14) = 5x + 2[/tex]

Open brackets

[tex]3x + 42 = 5x + 2[/tex]

Collect like terms

[tex]3x - 5x = 2 - 42[/tex]

[tex]-2x = -40[/tex]

Divide both sides by -2

[tex]x = 20[/tex]

Angle KNL is

[tex]\angle KNL =3(x + 14)[/tex]

Substitute 20 for x

[tex]\angle KNL =3(20 + 14)[/tex]

[tex]\angle KNL =3(34)[/tex]

[tex]\angle KNL =102[/tex]

Hence, the measure of KNL is 102 degrees.

Read more about angles in a transversal at:

https://brainly.com/question/18024908

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