Answer:
A. [tex] 82\degree[/tex]
Step-by-step explanation:
By the theorem of intersecting chords inside a circle.
[tex] m\angle OVU=\frac{1}{2} (m\widehat {GK} +m \widehat {OU}) [/tex]
[tex] m\angle OVU = \frac{1}{2} (142\degree + 54\degree) [/tex]
[tex] m\angle OVU=\frac{1}{2} \times 196\degree [/tex]
[tex] m\angle OVU = 98\degree [/tex]
[tex] m\angle OVU + m\angle OVU = 180\degree [/tex]
(Linear pair angles)
[tex]m\angle OVG + 98\degree = 180\degree [/tex]
[tex] m\angle OVG =180\degree - 98\degree[/tex]
[tex] m\angle OVG = 82\degree[/tex]
