Short Answer 33.
RemarkDraw AC on your paper diagram.
There are two facts that you have to use.
1. The first is that The arc measurement (7x - 2 in this case) is the same as the central angle.
2. The central angle is twice as big as the angle formed by <ABC. It does not matter where B is as long as it does not go above AC. Above means toward the top of your diagram.
GivensCentral Angle = 7x - 2
ABC = 2.5x + 4
Equation1/2(7x - 2) = 2.5x + 4 Remove the brackets.
3.5x - 1 = 2.5x + 4 Add 1 to both sides.
3.5x = 2.5x + 4 + 1
3.5x = 2.5x + 5 Subtract 2.5x from both sides.
3.5x - 2.5x = 5
x = 5
ConclusionFind the value of 7x - 2
Let x = 5
7x - 2
7(5) - 2
35 - 2
33 <<<< Answer