“lines that appear to be tangent are tangent. o is the center of the circle. what is the value of x? ”

To solve the problem we will first name all the points given to us, and then we will find ∠O, and then we will find the value of x.

The value of x is 22°.

Given to us

Looking at the diagram below,

In ΔAOB

OA =  OB = R, the radius of the circle O,

therefore, the ΔAOB is an isosceles triangle, with OA, OB as the congruent sides and AB as the base of the triangle.

Thus, ∠OAB = ∠OBA = 56°

Sum of all the angles of a triangle = 180°

∠O + ∠AOB + ∠OBA = 180°

We know ∠AOB = ∠OBA, therefore,

∠O + 2(∠AOB) = 180°

∠O + 2(56°) = 180°

∠O = 68°,

In ΔOBC,

BC is the tangent to the circle O, therefore,

∠OBC = 90°

Sum of all the angles of a triangle = 180°

∠O + ∠OBC + ∠OCB = 180°

68° + 90° + ∠OCB = 180°

∠OCB = 180° - 68° - 90°

∠OCB = 22°

Hence, the value of x is 22°.

Learn more about Triangle:

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step-by-step explanation:

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