Answer:
∠JKP = 35°
Step-by-step explanation:
since P is the incenter, then lines to incenter bisect the corner angles:
7x - 6 = 5x + 4
subtract 5 x from both sides of the equation:
2x - 6 = 4
add 6 to each side:
2x = 10
divide both sides by 2:
x = 5
∠KJP = 7(5) - 6 = 29°
∠LJP = 5(5) + 4 = 29°
then ∠KJL = 29° + 29° = 58°
∠KLJ = 26° + 26° = 52°
∠JKL = 180° - 58° - 52° = 70°
∠JKP = 1/2 ∠JKL = 1/2(70°) = 35°
there might be a more direct way about it but this was the least confusing way I know to explain it.
