Question

In the diagram below of triangle L, M, NLMN, OO is the midpoint of start overline, L, N, end overline
LN
and PP is the midpoint of start overline, M, N, end overline
MN
. If O, P, equals, minus, 7, plus, 2, xOP=−7+2x, and L, M, equals, minus, 2, x, plus, 40LM=−2x+40, what is the measure of start overline, O, P, end overline
OP
?
GPT 3.5
Since O is the midpoint of LN, we know that LO = ON. Therefore, we can write the following equation:

LO = ON
-2x + 40 = -7 + 2x

Solving for x, we get:
-4x + 80 = -14 + 2x
-6x = -94
x = 47/3

Now we can find the length of OP using the equation OP = -7 + 2x:
OP = -7 + 2(47/3)
OP = -7 + 94/3
OP = 81/3
OP = 27

Therefore, the measure of line OP is 27.

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