Final answer:
Angle 2 and Angle 7 are Alternate Exterior Angles, so they are equal. By setting the equations 4x + 24 and 12x - 8 equal and solving for x, we find x to be 4. Subsequently, by substituting x back into the expression for Angle 2, we determine the measure of Angle 2 to be 40 degrees.
Step-by-step explanation:
If Angle 2 and Angle 7 are Alternate Exterior Angles, then they are equal when two lines are parallel and are cut by a transversal. Thus, we can set the expressions for Angle 2 and Angle 7 equal to each other and solve for x.
Given that Angle 2 = 4x + 24 and Angle 7 = 12x - 8, we set up the equation:
4x + 24 = 12x - 8
To solve for x, we will subtract 4x from both sides and then add 8 to both sides:
4x + 24 - 4x = 12x - 8 - 4x
24 = 8x - 8
24 + 8 = 8x
32 = 8x
Dividing both sides by 8, we have:
x = 4
Now, we substitute x back into the expression for Angle 2:
Angle 2 = 4(4) + 24
Angle 2 = 16 + 24
Angle 2 = 40 degrees
Therefore, the measure of Angle 2 is 40 degrees.