Question

I am stuck on 14 and 15 as they do not have a straight line going through to help me, anybody know how to ?? thanks !

Answer 1

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°