P is the incenter of △JKL. Find m∠JKP. & can you please explain

Mathematics

1 answer:

dangina [55]3 years ago

7 0

Answer:

m∠MKP = 35°

Step-by-step explanation:

Incenter is the intersection of angle bisectors.

∠MJP = ∠OJP, ∠MKP = ∠NKP, ∠NLP = ∠OLP

First find the value of x:

7x - 6 = 5x + 4
7x - 5x = 4 + 6
2x = 10
x = 5

Find the angle MJP:

7*5 - 6 = 29°

We know sum of interior angles of a triangle is 180°. Using this find the missing angle measure:

2*m∠MJP + 2*m∠NJP + 2*m∠MKP = 180°
m∠MJP + m∠NJP + m∠MKP = 90°
29° + 26° + m∠MKP = 90°
m∠MKP = 90° - 55°
m∠MKP = 35°

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