Question

If mLM = (8x - 56) and mNP = (5x + 22), find mLP.

Answer 1

Sum of all 4 arcs is full circle which is 360 deg, can you go from there to set equation?

Answer 2

So.. \[360 = 8x-56+5x+22+39+mLP\]

Answer 3

Sorry, you need to consider first that the two larger arcs are of same measure. Because their perpendicular bisectors are of same length (as indicated in the picture).
Set the equation and solve for x

Answer 4

mLM and mMP are same

Answer 5

So... \[8x-56=5x+22\]\[3x=78\]\[x=26\]

Answer 6

Good, now you can go the the first equation and find the missing measure

Answer 7

Yes, correct

Answer 8

so LP would be 17?

Answer 9

Yes, this is the answer

Answer 10

Thanks :)

Answer 11

You are welcome!