O is the center of the given circle. The measure of angle O is 128°. The diagram is not drawn to scale. Assuming that lines that appear to be tangent are tangent, what is the value of x?

Solution:

We know that the measure of exterior angle is the semi difference of the arc it covers.

By central angle

m AB = 128°

By substituting it

m ACB = 360 - 128 = 232°

We know that

∠x = 1/2 × (m ACB - m AB)

Substituting the values

∠x = 1/2 × (232 - 128)

∠x = 1/2 × 104

∠x = 52°

Therefore, the value of x is 52°.

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O is the center of the given circle. The measure of angle O is 128°. The diagram is not drawn to scale. Assuming that lines that appear to be tangent are tangent, what is the value of x?

Summary:

O is the center of the given circle. The measure of angle O is 128°. The diagram is not drawn to scale. Assuming that lines that appear to be tangent are tangent, the value of x is 52°.