Adjacent Angles In Geometry: Definition, Properties, And Examples

Adjacent Angles

Angles that have a common side and a common vertex (corner point).

Adjacent angles are angles that share a common vertex and a common side. In other words, they are angles that are next to each other.

For example, in the figure below, $\angle ABC$ and $\angle CBD$ are adjacent angles since they share the common vertex $B$ and the common side $BC$.

[asy]
pair A,B,C,D;
A = (-1,1);
B = (0,0);
C = (0,1);
D = (1,0);
draw(A–B–C–D);
draw(B–D);
label($A$,A,SW);
label($B$,B,SW);
label($C$,C,NW);
label($D$,D,S);
label($\angle ABC$,B+(.15,.1));
label($\angle CBD$,B+(.15,-.1));
[/asy]

It’s important to note that adjacent angles do not overlap, meaning they share only one common side and do not share any interior points.

Adjacent angles can have different measures or they can be congruent. If the sum of the measures of two adjacent angles is 90 degrees, they are called complementary angles. If the sum of their measures is 180 degrees, they are called supplementary angles.

In summary, adjacent angles are angles that share a common vertex and a common side, but they do not overlap. They can have different measures or be congruent, and they can be complementary or supplementary depending on the sum of their measures.

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