Answer:
x = 8 and x = 5
Step-by-step explanation:
• The measure of an arc is equal to the measure of the central angle that subtends it.
(6)
9x + 13 = 85 ( subtract 13 from both sides )
9x = 72 ( divide both sides by 9 )
x = 8
(7)
The central angle AOC is equal to arc AC, that is
∠ AOC = 141°
The sum of the angles around a point is 360° , then
∠ BOC + ∠ AOC + ∠ AOB = 360° , that is
∠ BOC + 141° + 134° = 360°
∠ BOC + 275° = 360° ( subtract 275° from both sides )
∠ BOC = 85°
Then
arc BC = ∠ BOC ( substitute values )
16x + 5 = 85 ( subtract 5 from both sides )
16x = 80 ( divide both sides by 16 )
x = 5
