anonymous
  • anonymous
Quadrilateral BCDE is inscribed inside a circle as shown below. Write a proof showing that angles C and E are supplementary.
Geometry
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schrodinger
  • schrodinger
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anonymous
  • anonymous
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anonymous
  • anonymous
@rishavraj
anonymous
  • anonymous
i really need some help on this ive seen others like this question but the answer never made sense

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midhun.madhu1987
  • midhun.madhu1987
Since the 4 vertices of the quadrilateral BCDE lies on the circle...hence it is a Cyclic Quadrilateral.. The sum of the opposite angles of a cyclic quadrilateral is 180. Do you want the proof of this theorem??
anonymous
  • anonymous
yes please
midhun.madhu1987
  • midhun.madhu1987
http://nrich.maths.org/1310
anonymous
  • anonymous
could you explain it? @midhun.madhu1987
midhun.madhu1987
  • midhun.madhu1987
|dw:1438966898875:dw|
midhun.madhu1987
  • midhun.madhu1987
Angle BOD = 2 Angle BAD Angle BAD = (1/2) Angle BOD ----(1) Angle DOB = 2 Angle BCD Angle BCD = (1/2) Angle BCD ----(2) Adding both equations (1) and (2) Angle BAD + Angle BCD = (1/2) Angle BOD + (1/2) Angle BCD = (1/2) (Angle BOD + Angle BCD) = (1/2) * 360 = 180 Hope you got it

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