Question

Are AC and DF definitely parallel? How do you know?

Answer 1

Answer:

We know that,

Angle E = 123

Angle B = 57

We observe that,

Angle DEB and Angle E form a linear pair and are supplementary.

Angle DEB + Angle E = 180

Angle DEB = 180-123

=57

We know that if two lines are parallel, the corresponding angles are equal.

Conversely, if the corresponding angles are equal, then the two lines are parallel.

Here,

As Angle B and Angle DEB are corresponding angles are equal in measure (Angle B = Angle DEB = 57), we can say that Line AC and Line DF are parallel.