Answer:
x = 21.4
Step-by-step explanation:
An inscribed angle is the angle formed when two chords meet at one point on the circumference of a circle, and the intercepted arc is the arc that is between the endpoints of those chords.
In the given diagram, angle OMN is the inscribed angle, and arc ON is the intercepted arc.
According to the Inscribed Angle Theorem, the measure of an inscribed angle is half the measure of the intercepted arc.
Therefore:
[tex]m\angle OMN=\dfrac{1}{2}\;\overset{\frown}{ON}\\\\\\(5x - 47)^{\circ}=\dfrac{1}{2} \cdot 120^{\circ}\\\\\\5x-47=\dfrac{1}{2}\cdot120\\\\\\5x-47=60\\\\\\5x=107\\\\\\x=\dfrac{107}{5}\\\\\\x=21.4[/tex]
So, the value of x is:
[tex]\LARGE\boxed{\boxed{\vphantom{}x=21.4}}[/tex]
