Two transversals intersect two parallel lines as shown
a. what is the value of x?

b. what is the measure of angle LMN?

c. what is the measure of angle KLM?

d. which two triangles are similiar how do you know?

Step-by-step explanation:

a)  Two lines are parallel and KN is transversal.

So, alternate interior angles are equal.

∠LNM =∠JKL

6x + 1 = 25

Subtract 1 from both sides.

6x + 1 - 1 = 25 -1

6x = 24

Divide both sides by 6

6x/6 = 24/6

x = 4°

b) ∠LMN = 3x +11

              = 3*4 + 11

               = 12 + 11

∠LMN = 23°

c)  ∠KJL = ∠LMN    {Alternate interior angles are equal, transversal JM}

∠KJL = 23°

In ΔKLJ,

∠JKL + ∠KLM + ∠LJK = 180°

25 + ∠KLM + 23 = 180

∠KLM + 48 = 180

∠KLM = 180 - 48

∠KLM = 132°

d) In ΔJKL & ΔLMN

∠J = ∠M

∠K=∠N

∠NLM = ∠KLJ     {Vertically opposite angles.

ΔKJL & ΔLMN  are similar triangles

36 is the final answer! : )