For the following question, assume that lines that appear to be tangent are tangent. Point O is the center of the circle. Find the value of x. The figures are not drawn to scale. ∡O = 142°
38
58
44
218
The angle ∡O is an inscribed angle, which is half the measure of the central angle that subtends the same arc. Therefore, the central angle that subtends arc AB is 2 * 142° = 284°.
Since angle x is formed by a tangent and the chord AB, it is equal to half of the difference between the central angle and the inscribed angle:
x = 1/2 * (284° - 142°) = 1/2 * 142° = 71°
Therefore, the value of x is 71.
So, the closest answer option is:
58