If P is the incenter of triangle JKL find each measure

Check explanation section (check the attached file for the diagram to the question).

Step-by-step explanation:

Without mincing words let's dive straight into the solution to the question/ problem above.

From the question above, we have that the point p = the point at which the bisecting angle of the triangles meets, that is the term known as incenter.

So, we have that; 7x - 6 = 5x + 4. Hence;

2x = 10; x = 5°.  

Thus, the angle 5x + 4 = which is the angle KJP = 5x + 4. Recall from above that x = 5°.

Hence; 5x + 4 = 5(5) + 4 = 25 - 4 = 29°.

Also, the angle 7x - 6 = which is the angle KJP = 7x - 6. Recall from above that x = 5°.

Therefore, 7x - 6  = 7(5) - 6 = 35 - 6 = 29°.

The angle KJP + the angle LJP= the angle KJL.

Therefore, the angle KJL = 29° + 29° = 58°.

Angle KJL = 130 - ( angle KJL) - (angle KJL).

The angle KJL = 130° - ( 58°) - (52° ) = 70°