Answer
1) Angle LAP = Angle LAR = 76 degrees
2) Line AL dividing Angle PAR into two equal parts (Angle LAP and Angle LAR), is a bisector of Angle PAR.
Step-by-step explanation
Adjacent angles are angles that share the same side and a common vertex (that is, the same corner point) and don't overlap.
We are told that Angle LAP and Angle LAR are adjacent angles belonging to the vertex PAR.
This means that line AL divides Angle PAR into two parts; Angle LAP and Angle LAR.
Angle PAR = (Angle LAP) + (Angle LAR)
Angle PAR = 2 (3x + 7)
Angle LAP = 3x + 7
Angle LAR = 4 (x - 4)
Angle PAR = (Angle LAP) + (Angle LAR)
2 (3x + 7) = 3x + 7 + 4 (x - 4)
6x + 14 = 3x + 7 + 4x - 16
6x + 14 = 7x - 9
7x - 9 = 6x + 14
7x - 6x = 14 + 9
x = 23 degrees
Angle PAR = 2 (3x + 7) = 6x + 14 = 6(23) + 14 = 138 + 14 = 152 degrees
Angle LAP = 3x + 7 = 3 (23) + 7 = 76 degrees
Angle LAR = 4 (x - 4) = 4x - 16 = 4(23) - 16 = 92 - 16 = 76 degrees
Since Angle LAP = Angle LAR
It means that the line AL dividing Angle PAR into two equal parts (Angle LAP and Angle LAR), is a bisector of Angle PAR.
Hope this Helps!!!