Answer:
mLP = 17°
Step-by-step explanation:
The perpendicular bisectors from the center to the vertical lines are equal.
Therefore:
mLM = mNP
8x - 56 = 5x + 22
8x - 5x = 22 + 56
3x = 78
x = 78/3
x = 26
Note that:
mLM + mMN + mNP + mLP = 360° (sum of angles at a point)
(8x - 56) + 39 + (5x + 22) + mLP = 360
8x + 5x - 56 + 39 + 22 = 360
13x + 5 + mLP = 360
mLP = 360 - 5 - 13x
mLP = 355 - 13x
mLP = 355 - 13(26)
mLP = 355 - 338
mLP = 17°