By definition, two angles are adjacent if they share one side and the vertex.
To determine if ∠3 and ∠4 are adjacent, you have to look at each image and determine if they share the vertex and one side:
1.
In this image ∠3 and ∠4 share, the vertex but they do not share one side, this indicates that these angles are not adjacent.
2.
In this image ∠3 and ∠4 share the vertex and one side (blue line), which indicates that they are adjacent angles.
3.
In this image ∠3 and ∠4 share one side (blue line) but each angle has its own vertex (green dots). You cannot conclude these angles are adjacent.
4.
Two angles are complementary of they add up to 90º, they don't necesarly have to be adjacent.
Any acute angle, meaning, any angle that measures less than 90º, has a complement.
For example, you have the following angles:
- If both ∠1 and ∠2 are acute angles and complementary, then we know that they add up to 90º:
[tex]\angle1+\angle2=90º[/tex]
-For example, ∠1= 46º, then you can determine the measure of ∠2 as follows:
[tex]\begin{gathered} \angle2=90º-\angle1 \\ \angle2=90-46 \\ \angle2=44º \end{gathered}[/tex]
Both ∠1=46º and ∠2=44º are acute and add up to 90º
-If one of the angles is a right angle, for example, ∠2=90º, then no matter what measure does ∠1 take, they will never add up to 90º.
We can say that right angles do not have a complement.
-If one of the measures of the angles is more than 90º (it is an obtuse angle), let's say, for example, ∠1= 124º, no matter what measure ∠2 has, if you add both angles, they will never add up to 90º.
So we can say that obtuse angles have no complements.
In conclusion, not all angles can have a complement, only acute angles have complements.
