Find the measure of the arc or angle indicated. Provide a perfect solution.
Given: Arc JK = 140, Arc LJ = 60
Need: Angle J
Choices:
A) 88
B) 80
C) 70
D) 92
B) 80
Solution:
Since the sum of the measures of the arcs is equal to the measure of the angle, we can use the following equation to solve for the measure of angle J:
Arc JK + Arc LJ = Angle J
140 + 60 = 200
Therefore, the measure of angle J is 200 degrees. Since a full circle is 360 degrees, we can subtract 200 from 360 to find the measure of angle J:
360 - 200 = 160
Therefore, the measure of angle J is 160 degrees, or 80 degrees (since angles are measured in degrees). Therefore, the correct answer is B) 80.