. Segment CB is tangent to the circle, and m<C = 18 degrees. Solve for x.

Question

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18 degrees
90 degrees
112 degrees
72 degrees

Answer 1

72 degrees

Since angle C is an angle inscribed in the circle and segment CB is a tangent to the circle, we can determine that angle C is half of the intercepted arc angle AB. Therefore, angle AB = 2*18 = 36 degrees.

Since angle ACB is 90 degrees (tangent and radius are perpendicular), angle ACB = 90 - 36 = 54 degrees.

Now, since segment AB is a straight line, angle A + angle ACB = 180 degrees.

Therefore, x + 54 = 180, x = 126 degrees.