By using the property of incenter, measures of the sides and the angles will be,
JK = 21.2 units
KL = 26.63 units
JL = 28.33 units
m∠K = 36°
By the property of incenter,
PM = PN = PO = 7 units
∠MJP = ∠OJP = 32°
∠NLP = ∠OLP = 22°
By 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°
From ΔJMP,
tan(32°) = [tex]\frac{MP}{MJ}[/tex]
tan(32°) = [tex]\frac{7}{MJ}[/tex]
MJ = [tex]\frac{7}{\text{tan}(32)^\circ}[/tex]
MJ = 11.20
From ΔPOL,
tan(22°) = [tex]\frac{OP}{OL}[/tex]
tan(22°) = [tex]\frac{7}{OL}[/tex]
OL = 17.33
From ΔKNP,
tan(36°) = [tex]\frac{NP}{KN}[/tex]
tan(36°) = [tex]\frac{7}{KN}[/tex]
KN = 9.63
Therefore, JK = MJ + MK = 21.2 units
KL = LN + KN = 26.63 units
JL = JO + OL = 28.33 units
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