Assume that lines that appear to be tangent are tangent. Point O is the center of the circle. Find the value of x if the m<P = 28 (1 point) Responses 62 degrees 62 degrees 68 degrees 68 degrees 66 degrees 66 degrees 64 degrees
62 degrees
Angle POQ is equal to 2 times angle P. This is because angle POQ is an inscribed angle and angle P is the angle that subtends the same arc. Therefore, angle POQ = 2(28) = 56 degrees.
Since angle POQ is an exterior angle of triangle POQ, it is equal to the sum of the two non-remote interior angles. Therefore, x + 28 = 56. Solving for x gives x = 28 degrees.
Therefore, the value of x is 28 degrees.