Section: Math

78)

In the figure, F, G, H, and J are collinear. Line segments FG, GK, and HK, are of equivalent length and the measure of angle JHK is 120 degrees. What is the degree measure of angle FKG?

1. 30 degrees
2. 45 degrees
3. 60 degrees
4. 120 degrees

Answer 1 is correct. Angle JHK is 120 degrees, which makes Angle GHK 60 degrees. Since line segments GK and HK are congruent, they have the same degree measurements at the angle points. That makes Angle GKH 60 degrees as well. Now you just have to solve for the remaining triangle. Because Angle HGK is 60 degrees, Angle FGK will be 120 degrees. (There are 180 degrees in a triangle.) The remaining 60 degrees needed to complete the triangle's measurements will have to be divided by the two remaining angles, which we know to be equal. So 60 degrees divided by two is 30 degrees.