We have a + b = 180 and a = 12 + b;
Then, 12 + b + b = 180;
12 + 2b = 180;
2b = 168;
b = 84;
a = 12 + 84;
a = 96;
Answer:
C) They are perpendicular lines.
Step-by-step explanation:
We first need to find the slope of the graph of the lines passing through these points using:

The slope of the line that passes through (−12, 15) and (4, −5) is


The slope of the line going through (−8, −9) and (16, 21) is



The product of the two slopes is

Since

the two lines are perpendicular.
Distribute 2 and remove parentheses :
1/2x+8=3x-6
Multiply both sides of equation by 2:
x+16=6x-12
Move terms:
x+16-6x=-12
x-6x=-12-16
Collect like terms:
-5x=-28
Divide both sides:
x=28/5
Refer to the diagram below
If we draw a line that connects the center of rotation to one of the points, say point N, and take this line as the 0° position, then we need three 'turn' of 90° to get to 270°.
Coordinate of N' (-3, 4)
Coordinate of M' (-9, 5)