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s2008m [1.1K]
3 years ago
13

In ⊙O, ST and VT are tangents. m∠STV = 22°. Find the value of a, b, and m∠SOV.

Mathematics
1 answer:
Rasek [7]3 years ago
6 0

Answer:

\huge \orange {\boxed {a =202\degree}}

\huge \purple {\boxed { b = 158\degree}}

\huge \red {\boxed {m\angle SOV = 158\degree}}

Step-by-step explanation:

In \odot O, ST and VT are tangents at points S and V respectively.

\therefore OS\perp ST, \:and\: OV\perp VT

\therefore m\angle OST=m\angle OVT = 90\degree

In quadrilateral OSTV,

m\angle SOV +m\angle OST+m\angle OVT+m\angle STV = 360\degree

(By interior angle sum postulate of a quadrilateral)

m\angle SOV +90\degree +90\degree +22\degree  = 360\degree

m\angle SOV +202\degree  = 360\degree

m\angle SOV = 360\degree-202\degree

\huge \red {\boxed {m\angle SOV = 158\degree}}

\because b = m\angle SOV

(Measure of minor arc is equal to measure of its corresponding central angle)

\huge \purple {\boxed {\therefore b = 158\degree}}

\because a + b= 360\degree

(By arc sum property of a circle)

\therefore a = 360\degree - b

\therefore a = 360\degree -158\degree

\huge \orange {\boxed {\therefore a =202\degree}}

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