Geometry help?

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3 Answers
Mar 30, 2018

x=1623

Explanation:

MOP is similar to MLN because all the angles of both triangles are equal.
This means that the ratio of two sides in one triangle will be same as that of another triangle so MOMP=MLMN
After putting in values, we get x15=x+2015+18

x15=x+2033

33x=15x+300

18x=300

x=1623

Mar 30, 2018

C

Explanation:

We can use the Side-Splitter Theorem to solve this problem. It states:

  • If a line is parallel to a side of a triangle and intersect the other two sides, then this line divides those two sides proportionally.

Since OP || LN, this theorem applies.

So we can set up this proportion:
x20=1518

Now cross multiply and solve:
x20=1518

x×18=20×15

18x=300

x=300181612181623

So the answer is C

Mar 30, 2018

Answer: x=1623

Explanation:

Since OP is parallel to LN, we know that MOP=MLN and MPO=MNL from the Corresponding Angles Theorem

Further, we also have that OMP=LMN since they are the same angle.

Therefore OMP is similar to LMN (OMP~LMN)

Since similar triangles have the same side length ratio:
MOML=MPMN

Plugging numbers in, we have:
xx+20=1515+18

We can now solve this equation by cross multiplication:
33x=15(x+20)
33x=15x+300
18x=300
x=1623