Question

Quadrilateral BCDE is inscribed inside a circle as shown below. Write a proof showing that angles C and E are supplementary.

Answer 1

@rishavraj

Answer 2

i really need some help on this ive seen others like this question but the answer never made sense

Answer 3

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??

Answer 4

yes please

Answer 5

http://nrich.maths.org/1310

Answer 6

could you explain it? @midhun.madhu1987

Answer 7

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