Question

If the measure of an intercepted arc is 118°, and the measure of the inscribed angle is 2x - 1, what is the equation to find the value of x?

2 x - 1 = 2(118°)
2(2 x - 1) = 118°
2 x - 1 = 118°

Answer 1

An inscribed angle equals half its intercepted arc, so (2x − 1) = 118°/2 = 59°. Equivalently multiply both sides by 2: 2(2x − 1) = 118°. (Solving gives x = 30.)