Answer:
AC = 33°
Step-by-step explanation:
The measure of the inscribed angle ABC is half the measure of its intercepted arc AC , that is
∠ ABC = [tex]\frac{1}{2}[/tex] AC ( substitute expressions )
2.5x + 4 = [tex]\frac{1}{2}[/tex] (7x - 2) ← multiply both sides by 2 to clear the fraction
5x + 8 = 7x - 2 ( subtract 5x from both sides )
8 = 2x - 2 ( add 2 to both sides )
10 = 2x ( divide both sides by 2 )
5 = x
substitute x = 5 into the expression for AC
AC = 7x - 2 = 7(5) - 2 = 35 - 2 = 33°
