Answer:
AC = 33°
Step-by-step explanation:
Given:
Arc AC = (7x - 2)°
m<ABC = (2.5x + 4)°
Required:
Measure of arc AC
Solution:
Based on the inscribed angle theorem,
m<ABC = ½(AC)
Substitute
2.5x + 4 = ½(7x - 2)
Multiply both sides by 2
2(2.5x + 4) = 7x - 2
5x + 8 = 7x - 2
Collect like terms
5x - 7x = -8 - 2
-2x = -10
Divide both sides by -2
x = -10/-2
x = 5
✔️Arc AC = (7x - 2)°
Substitute the value of x
AC = 7*5 - 2
AC = 35 - 2
AC = 33°
