Answer:
ML = 10
Explanation:
Given:
LN = ML + 2
JL = 15
LK = 18
We use AAA Similarity Criterion: If two triangles are equiangular, then they are similar. By equiangular, it means that the measurements of the corresponding angles of the two triangles are equal. It is also called the Angle Angle Similarity Theorem.
If lines MN and JK are parallel, then ∠LMN=∠LJK and ∠LNM=∠LKJ and hence ΔMLN∼ΔJLK. Based on the proportionality of the sides, we compose an equation and solve it:
LK/JL = LN/ML
18/15 = LN/ML
6/5 = LN/ML
Since LN = ML + 2, the equation can be written:
6/5 = (ML + 2)/ML
6/5 = 1 + 2/ML
1/5 = 2/ML
ML/5=2
ML=10