Answer:
14. x=21, GK=167°, HJ=98°, HGJ=262°, GKJ=201°
15. x=9, AD=108°, BC=23°, DC=139°, DBC=221°
Step-by-step explanation:
In each case, the sum of the arcs around the circle is 360°.
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14. 61 +(5x -7) +34 +(9x -22) = 360
14x = 294 . . . . . subtract 66, simplify
x = 21 . . . . . . . . divide by 14
(5x -7) = 98
(9x -22) = 167
- x = 21
- arc GK = 167°
- arc HJ = 98°
- arc HGJ = 360° -98° = 262°
- arc GKJ = 167° +34° = 201°
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15. 90 +(2x +5) +(17x -14) +(12x) = 360
31x = 279 . . . . subtract 81, simplify
x = 9 . . . . . . . . divide by 31
(2x+5) = 23
(17x -14) = 139
(12x) = 108
- x = 9
- arc AD = 108°
- arc BC = 23°
- arc DC = 139°
- arc DBC = 360° -139° = 221°
