An angle whose vertex is on a circle and whose sides are chords of the circle is an inscribed angle. Therefore, in the given diagram ∠ X is an inscribed angle. Also, VW is its intercepted arc. Let a^(∘) and b^(∘) be the measures of VW and VX, respectively.
According to the Inscribed Angle Theorem, the measure of an inscribed angle is half the measure of its intercepted arc.
This means that 14 is half of a.
We found that a=28. Let's pay close attention to VW and VX.
An arc whose endpoints are the endpoints of a diameter has a measure of 180^(∘). Therefore, by the Arc Addition Postulate the sum of 28 and b is equal to 180.
28+b=180 ⇔ b=152
Hence, the measure of the minor arc VX is 152^(∘).
