Answer:
measure of Arc FJ is 80 degrees.
Step-by-step explanation:
Key skills: High School Geometry, One Variable Equations, Angles
1)Let's look at the diagram thoroughly
2) The 2 thing we can get are:
- Angle HKG and Angle IKJ are vertical angles (which means they are congruent).
- Angle HKG + Angle GKF + Angle FKJ = 180 (Since they all form a straight angle - A straight angle is 180 degrees in measure.)
3) First we can use the fact that Angle HKG and Angle IKJ are vertical angles. This makes them congruent (Or equal in size)
- We can then solve for x by making the equation: 3x-22=x+10
4) Solve this by moving the x's to one side, and the numbers to the other. You would then get: 3x-x=10+22
3x-x= 2x 10+22=32
2x=32
Divide by 2 on both sides and x=16.
5) We get that x=16. Now to find the measure of Arc FJ, we need to use the fact that Angle HKG + Angle GKF + Angle FKJ = 180
What we want to find is Angle FKJ. The measure of Angle FKJ would be the measure of Arc FJ
6) We can make an equation: x+10+74+Angle FKJ=180
- Solve this --> x=16, so substitute it in
- 16 + 10 + 74 + Angle FKJ=180
- 100 + Angle FKJ = 180
- Angle FKJ = 80 degrees
If Angle FKJ is 80 degrees, then Arc FJ measures 80 degrees.
Hope you understood! Have a Nice Day! :D
