Although part of your question is missing, you might be referring to this full question: If P is the incenter of ΔJKL, find each measure (triangle as attached).
Based on the property of incenter, the measurements of the sides and the angles will be:
JK = 21.2 units
KL = 26.63 units
JL = 28.33 units
m∠K = 36°
By using the property of incenter:
PM = PN = PO = 7 units
∠MJP = ∠OJP = 32°
∠NLP = ∠OLP = 22°
By using the triangle sum theorem,
m∠JKL + m∠KLJ + m∠LJK = 180°
2(m∠NKP) + 2(m∠NLP) + 2(m∠MJP) = 180°
2(m∠NKP) + 2(22°) + 2(32°) = 180°
2(m∠NKP) = 180° - 108°
m∠NKP = 36°
Then, from ΔJMP,
tan(32°) = MP/MJ
tan(32°) = 7/MJ
MJ = 7/tan(32)°
MJ = 11.20
And from ΔPOL,
tan(22°) = OP/OL
tan(22°) = 7/OL
OL = 17.33
And from ΔKNP,
tan(36°) = NP/KN
tan(36°) = 7/KN
KN = 9.63
Hence, JK = MJ + MK = 21.2 units
KL = LN + KN = 26.63 units
JL = JO + OL = 28.33 units
Learn more about incentre of triangle at: https://brainly.com/question/29634968
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