The sum of the measures of all the arcs in a circle is 360°
So... looking at the circle in problem #9....we can make the following equation:
61° + (5x - 7)° + 34° + (9x - 22)° = 360°
Remove the degree sign from every term.
61 + 5x - 7 + 34 + 9x - 22 = 360
Combine like terms.
14x + 66 = 360
Subtract 66 from both sides of the equation.
14x = 294
Divide both sides of the equation by 14
x = 21
Now that we know what x is, we can find the measures of all the arcs.
m⌢GK=(9x−22)∘=(9(21)−22)∘=167∘ m⌢HJ=(5x−7)∘=(5(21)−7)∘=98∘ m⌢HGJ=m⌢HG+m⌢GK+m⌢KJ=61∘+167∘+34∘=262∘ m⌢GKJ=m⌢GK+m⌢KJ=167∘+34∘=201∘