Final answer:
An inscribed angle should be half the measure of its intercepted arc; with an inscribed angle of 19 degrees, the intercepted arc should measure 38 degrees, not 118 degrees, suggesting a possible error or misunderstanding in the question.
Step-by-step explanation:
To determine the measure of each variable given that an inscribed angle measures 19 degrees and its intercepted arc BC measures 118 degrees, we apply the basic property of inscribed angles and their intercepted arcs. By this property, an inscribed angle is half the measure of its intercepted arc. Therefore, if the inscribed angle measures 19 degrees, the intercepted arc would logically measure 2 x 19 degrees, which equals 38 degrees. However, in this problem, the intercepted arc is given as 118 degrees.
It seems there's a discrepancy here, or perhaps a misunderstanding of the question. If the inscribed angle is indeed 19 degrees, the intercepted arc cannot be 118 degrees unless there's another inscribed angle that also intercepts arc BC, which together with the 19-degree angle adds up to form the full measure of arc BC. This would imply the presence of an exterior angle to the circle measuring 118 degrees, but this detail is not provided in the question.
Therefore, without further information or clarification, it's not possible to correctly find the measure of the angle or the arc described in the question, and seems like there might be an error or misunderstanding in the materials or question presented.