The measure of the unknown arc ('X') is 189 degrees, determined by subtracting the sum of the given arc measures (96 degrees and 75 degrees) from the total degrees in a circle (360 degrees). Here option D is correct.
To determine the measure of the unknown arc ('X'), we need to consider that the total degrees in a circle is 360 degrees.
Given that the arc with a measure of 96 degrees is in the west direction and is followed by an arc of 75 degrees, we can find the measure of the unknown arc ('X') by subtracting the sum of these known arc measures from the total degrees in a circle.
X = 360 degrees - (96 degrees + 75 degrees) = 360 degrees - 171 degrees = 189 degrees.
Therefore, the measure of the unknown arc ('X') is 189 degrees.
So, the correct option is:
D - 189 degrees.
Complete question:
What is the measure of the unknown arc if the arc with a measure of 96° is in the west direction and the arc with a measure of 75° is followed by an unknown arc (denoted as 'X')?
A - 114 degrees
B - 226.5 degrees
C - 150 degrees
D - 189 degrees