Answer:
a. Value of x: 4
b. Measure of ∠LMN: 23
c. Measure of ∠KLM: 132
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
