Are vertical angles supplementary angles?

1 Answer
Dec 28, 2015

Vertical and supplementary are different relationships between angles.
However, there is a special case when vertical angles are supplementary as well - when these angles are right ones.

Explanation:

Vertical angles are formed by two intersecting lines. On a picture below angles #/_A# are vertical, as well as angles #/_B#.

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Supplemental angles are those that, if positioned adjacent to each other, form a straight angle.
On a picture below angles #/_KML# and #/_KMH# are supplemental since together they form a straight angle #/_LMH#.

enter image source here

In one particular case, when vertical angles are right angles (that is, lines that form this pair of vertical angles are perpendicular), their sum is equal to a straight angles and, therefore, they are supplemental.
See the picture below that represents angles formed by perpendicular lines.
Angles #/_1# and #/_3# are vertical, as well as angles #/_2# and #/_4#. In addition, since lines are perpendicular to each other, all angles are congruent. Therefore, each of these pairs is also a pair of supplemental angles since their sum is a straight_ angle.

enter image source here