FIND MISSING ANGLES CREATED BY TANGENT LINES OF CIRCLE

Find the value of x in each diagram. The lines AB and AC are tangents.

Problem 1 :

Solution :

BOA + BAO + OBA = 180º

x + 27º + 90º = 180º

x + 117º = 180º

x = 180º - 117º

x = 63º

So, the value of x is 63º.

Problem 2 :

Solution :

BOA + BAO + OBA = 180º

68º + x + 90º = 180º

x + 158º = 180º

x = 180º - 158º

x = 22º

So, the value of x is 22º.

Problem 3 :

Solution :

154 + ∠OAB = 180

∠OAB = 180 - 154

∠OAB = 26

AOB + OBA + BAO = 180º

x + 90 + 26 = 180

x + 116 = 180º

x = 180º - 116º

x = 64º

So, the value of x is 64º.

Problem 4 :

Solution :

Let ABO

ABO + BOA + OAB = 180º

90º + 2x + x = 180º

3x + 90º = 180º

3x = 180º - 90º

3x = 90º

Dividing 3 on both sides.

3x/3 = 90º/3

x = 30º

So, the value of x is 30º.

Problem 5 :

Solution :

In the quadrilateral ABOC,

∠BAC + ACO + ∠COB + ∠OBA = 360

x + 90 + 158 + 90 = 360

x + 338 = 360

x = 360 - 338

x = 22

Problem 6 :

Solution :

In the quadrilateral ABOC,

∠BAC + ACO + ∠COB + ∠OBA = 360

15 + 90 + x + 90 = 360

x + 195 = 360

x = 360 - 195

x = 165

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