Exterior Angles of a transversal
Exterior Angles are created where a
transversal
crosses two (usually parallel) lines.
Each pair of these angles are outside the parallel lines, and on the same side of the transversal.
Try this Drag an orange dot at A or B. Notice that the two exterior angles shown are
supplementary (add to 180°) if the lines PQ and RS are parallel.
Referring to the figure above, the
transversal AB crosses the
two lines PQ and RS, creating intersections at E and F.
Each pair of exterior angles are outside the parallel lines and on the same side of the transversal.
There are thus two pairs of these angles.
In the figure above, click on 'Other angle pair' to visit both pairs of exterior angles in turn.
Remember: exterior means outside the parallel lines.
The parallel case
If the transversal
cuts across parallel lines (the usual case) then exterior angles are supplementary (add to 180°).
So in the figure above, as you move points A or B, the two angles shown always add to 180°.
Try it and convince yourself this is true.
In the figure above, click on 'Other angle pair' to visit both pairs of exterior angles in turn.
The nonparallel case
If the transversal
cuts across lines that are not parallel, the exterior angles still add up to a constant angle, but the sum is not 180°.
Drag point P or Q to make the lines nonparallel. As you move A or B, you will see that the exterior
angles add to a constant, but the sum is not 180°.
(The angles are rounded off to the nearest degree for clarity, so bear that in mind if you check this).
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Other parallel topics
General
Angles associated with parallel lines
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