Respuesta :

Answers:

  1. Angle C = 95 degrees
  2. Angle D = 72 degrees
  3. Angle F = 108 degrees
  4. Arc CFE = 216 degrees

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Explanations:

  1. For any inscribed quadrilateral like this, the opposite angles are always supplementary. So that means C+E = 180. Plugging in E = 85 leads to C = 95.
  2. Angle D is an inscribed angle that subtends arc CFE. By the inscribed angle theorem, the inscribed angle is half that of the arc it cuts off, so angle D is half of 144 degrees at 144/2 = 72 degrees.
  3. Use the idea mentioned in problem 1. So we'll have F+D = 180. Plug in D = 72 to find that F = 108.
  4. Arcs CDE and CFE form a full circle. So the arc measures must add to 360 degrees. We simply subtract 144 from 360 to get the answer 216. As an alternative, you can use the idea mentioned in problem 2, but work in reverse.