Question

Suppose that angle LAP and angle LAR are adjacent angles, angle LAP= 3x +7, angle LAR = 4(x-4), And angle PAR = 2(3x+7). What can you conclude about line AL?

Answer 1

AL is a bisector

Explanation:

LAP = 3x+ 7

LAR = 4(x - 4) = 4x - 16

PAR = 2(3x + 7) = 6x + 14

If you see the figure I drew (something you should infer from the problem.

LAP + LAR = PAR

3x + 7 + 4x - 16 = 6x + 14

3x + 4x - 6x = 14 + 16 - 7

x = 23

LAP = 3 * 23 + 7 = 76

LAR = 4 * 23 - 16 = 76

Meaning line AL is dividing PAR into 2 equal parts