Line EK is a secant for AB and CD, E lies on AB, K belongs to CD.

Line EK is a secant for AB and CD, E lies on AB, K belongs to CD. Angle AEK = 49 degrees. At what value of the angle SKE can lines AB and CD be parallel?

Given: Direct EK secant for AB and CD;
E lies on AB4
K belongs to CD;
angle AEK = 49 degrees
AB parallel to CD
Find the value of the angle СKE -?
Solution: Angle AEK and angle EKC are one-sided for parallel straight lines AB and CD and secant EK. Then
angle AEK + angle EKC = 180 degrees;
49 degrees + EKS angle = 180 degrees;
angle EKC = 180 degrees – 49 degrees;
angle EKC = 131 degrees.
If the angle EKC is equal to 131 degrees, then lines AB and CD will be parallel.
Answer: at an angle EKC = 131 degrees.