Answer:
[tex]\huge \orange {\boxed {a =202\degree}} [/tex]
[tex] \huge \purple {\boxed { b = 158\degree}} [/tex]
[tex]\huge \red {\boxed {m\angle SOV = 158\degree}} [/tex]
Step-by-step explanation:
In [tex] \odot[/tex] O, ST and VT are tangents at points S and V respectively.
[tex] \therefore OS\perp ST, \:and\: OV\perp VT[/tex]
[tex] \therefore m\angle OST=m\angle OVT = 90\degree [/tex]
In quadrilateral OSTV,
[tex] m\angle SOV +m\angle OST+m\angle OVT+m\angle STV = 360\degree [/tex]
(By interior angle sum postulate of a quadrilateral)
[tex] m\angle SOV +90\degree +90\degree +22\degree = 360\degree [/tex]
[tex] m\angle SOV +202\degree = 360\degree [/tex]
[tex] m\angle SOV = 360\degree-202\degree [/tex]
[tex]\huge \red {\boxed {m\angle SOV = 158\degree}} [/tex]
[tex] \because b = m\angle SOV[/tex]
(Measure of minor arc is equal to measure of its corresponding central angle)
[tex] \huge \purple {\boxed {\therefore b = 158\degree}} [/tex]
[tex] \because a + b= 360\degree [/tex]
(By arc sum property of a circle)
[tex] \therefore a = 360\degree - b[/tex]
[tex] \therefore a = 360\degree -158\degree[/tex]
[tex]\huge \orange {\boxed {\therefore a =202\degree}} [/tex]
