have circle with lines AB intersecting line DC.

Question

solve for z.  arc AD = 40 degrees, <DEB = 124 degrees.  Both lines intersect at E.  Point E is not in center of circle.  Arc z = BC.

 

                      D                 B      draw a circle A>C, >B, >D

 

                               E                 draw a line A to B, C to D

 

                      A                  C      arc AD = 40

                                                  <DEB = 124

                                                  arc z = ?  arc BC

 

Answer 1

∠AED = 56°

∠AED = 0.5( arc AD + arc BC)

56° = 0.5( arc AD + arc BC)

112° = arc AD + arc BC

112° = 40° + arc BC

72° = arc BC