The angle pairs listed in the image can be named according to the special position they occupy when two transversals intersect four straight lines as follows:
Corresponding Angles (to be labelled pink):
∠1 and ∠3∠7 and ∠15∠4 and ∠12∠14 and ∠16
∠1 and ∠3
Alternate Interior Angles (to be labelled blue):
∠2 and ∠13∠8 and ∠11∠4 and ∠5∠11 and ∠14
Alternate Exterior Angles (to be labelled yellow):
∠5 and ∠10∠2 and ∠7 ∠3 and ∠16∠1 and ∠14
Consecutive Interior Angles (to be labelled green):
∠8 and ∠15∠12 and ∠14∠6 and ∠13∠3 and ∠5 ∠4 and <11
No Relationship (uncolored):
∠1 and ∠16∠3 and ∠15∠4 and ∠13∠6 and ∠16∠1 and ∠11∠7 and ∠13
The following are the special angle pairs that we can observe that are formed when a transversal intersects two straight lines:
Corresponding Angles:
The angles lie in the relative same position along the transversal that intersects each of their lines.
In the image given, the corresponding angles that are formed which are part of the angle pairs listed are:
∠1 and ∠3∠7 and ∠15∠4 and ∠12∠14 and ∠16
∠1 and ∠3
Alternate Interior Angles:
These are angles formed on opposite side of the transversal but lie within the two lines that are intersected.
In the image given, the alternate interior angles that are formed which are part of the angle pairs listed are:
∠2 and ∠13∠8 and ∠11∠4 and ∠5∠11 and ∠14
Alternate Exterior Angles:
These are angles formed on opposite side of the transversal but lie outside the two lines that are intersected.
In the image given, the alternate exterior angles that are formed which are part of the angle pairs listed are:
∠5 and ∠10∠2 and ∠7 ∠3 and ∠16∠1 and ∠14
Consecutive Interior Angles:
These are angles formed on the same side of the transversal but lie within the two lines that are intersected.
In the image given, the consecutive interior angles that are formed which are part of the angle pairs listed are:
∠8 and ∠15∠12 and ∠14∠6 and ∠13∠3 and ∠5 ∠4 and ∠11
No Relationship:
The angles that do not have any special relationship because of their relative positions are -
∠1 and ∠16∠3 and ∠15∠4 and ∠13∠6 and ∠16∠1 and ∠11∠7 and ∠13
In summary, the angle pairs listed in the image can be named according to the special position they occupy when two transversals intersect four straight lines as follows:
Corresponding Angles (to be labelled pink):
∠1 and ∠3∠7 and ∠15∠4 and ∠12∠14 and ∠16
∠1 and ∠3
Alternate Interior Angles (to be labelled blue):
∠2 and ∠13∠8 and ∠11∠4 and ∠5∠11 and ∠14
Alternate Exterior Angles (to be labelled yellow):
∠5 and ∠10∠2 and ∠7 ∠3 and ∠16∠1 and ∠14
Consecutive Interior Angles (to be labelled green):
∠8 and ∠15∠12 and ∠14∠6 and ∠13∠3 and ∠5 ∠4 and <11
No Relationship (uncolored):
∠1 and ∠16∠3 and ∠15∠4 and ∠13∠6 and ∠16∠1 and ∠11∠7 and ∠13
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