Lines BC and ED are parallel. They are intersected by transversal AE, in which point B lies between points A and E. Lines BC and ED are also intersected by transversal EC. Angle ABC measures 70 degrees, and angle CED measures 30 degrees. What angle relationship describes angles BCE and CED?

Alternate interior angles

Alternate exterior angles

Corresponding angles

Same-side interior angles

The image showing the lines is missing, so i have attached it.

m∠BCE = m∠CED = 30° ; Alternate interior angles

Step-by-step explanation:

We are given that:

Line BC and line ED are parallel measure of angle ABC: m∠ABC = 70° measure of angle CED; m∠CED = 30

Looking at the image attached, since line BC and line ED are parallel and transverse line AE intersects both of them, from corresponding angles theorem, we can say that angle BEC will be equal to angle ABC. Thus, BEC = 70°

Angle CED is given as 30°

From principle of alternate interior angles, angle BCE is equal to Angle CED.

Thus,

m∠BCE = m∠CED = 30°