Question

Check my work

Answer 1

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

Answer 2

My work :
The first thing i did was i drew a line from A to each of the vertex's. This resulted in four isosceles triangles. All four of the triangles have equal bases. The four isosceles triangle i labeled a,b,c,d.

Quadrilateral BCDE = 360

2a + 2b + 2c + 2d = 360

a + b + c + d = 180

(a+d) + (b+c) = 180

Angles E and C measure 180 proving that they are supplementary

Answer 3

@welshfella can you help me again?

Answer 4

the first statment is wrong 2a + ... adds up to 720 degrees.

the best way si as follows

Answer 5

use the theorem The angle subtended by a chord at the center of circle = 2 * angle subtended on the circle

So in the above diagram
<EAC = 2 * EBC

and reflex < EAC = 2 * <EDC

Answer 6

i am comply lost so far

Answer 7

And how many degrees are in <EAC + reflex < EAC?

Answer 8

would it be 180 degrees ?

Answer 9

the angle at the center = 2 * angle EBC