Answer:
The lines blue and green are perpendicular
Step-by-step explanation:
we know that
If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is -1)
The formula to calculate the slope between two points is equal to

step 1
Find the slope of the blue line
we have the points
(-1,-3) and (0,3)
substitute


step 2
Find the slope of the red line
we have the points
(3,-3) and (4,2)
substitute


step 3
Find the slope of the green line
we have the points
(-4,-1) and (2,-2)
substitute


step 4
Compare the slopes
Blue line ----> 
Red line ----. 
Green line ---> 
so
The slope of the blue line and the green line are opposite reciprocal ( their product is equal to -1)
therefore
The lines blue and green are perpendicular
Answer:
36
Step-by-step explanation:
AOB + BOC = AOC
AOC = 90 since the lines are perpendicular
6x-12 + 3x+30 = 90
Combine like terms
9x + 18 = 90
Subtract 18 from each side
9x+18-18 = 90-18
9x = 72
divide by 9
9x/9 = 72/9
x = 8
AOB = 6x - 12
= 6*8 - 12
= 48 -12
= 36