Shapes are important in our lives, and geometry deals with shapes, angles, and triangles. It is a branch of mathematics that is indispensable to human understanding. There are several types of angles, such as acute angles, obtuse angles, right angles, etc. An angle is formed by two rays that meet at a point with one common endpoint. Additionally, each of these types of angles can be broken down into pairs, such as supplementary angles, complementary angles, linear angles, opposite angles, and adjacent angles. A pair of angles that have a common arm and vertex is called an adjacent angle.
Moreover, angles that are adjacent to each other are also called adjacent angles. The common feature of these angles is that they never overlap. In a box of two pizza slices, their corners are in the middle. The whole pizza offers so many adjacent angles that there are two possible adjacent angles per slice. A slice of pizza has two possible adjacent angles attached. Complementary angles are those where the sum of adjacent angles equals 90 degrees. A pair of adjacent angles are supplementary if their sum is 180 degrees.
Types of adjacent angles:
- Complementary angles: If the sum of two angles is 90 degrees, then these are said to be complementary angles. When two complementary angles are adjacent, they become a right angle. Also, if two lines intersect and form four angles opposite to one another, these are called opposite angles. In this sense, complementary angles are also known as opposite angles.
- Supplementary angles: When two angles are adjacent to each other, they are called supplementary angles. When two angles are supplementary, they have 180° degrees in common.
How to identify an adjacent angle?
As you probably already know, adjacent angles must share both a side and a vertex. Therefore, if there is a third angle in between two angles coming from one corner, it means they don’t share any sides. Because they don’t share a vertex as well as aside, they are not adjacent angles.
Properties of adjacent angles:
- They are connected by a common vertex and by a common arm
- There are no overlaps between adjacent angles
- A common interior point does not exist
- If adjacent angles have a common vertex, then they can be complementary or supplementary
- An arm other than the common arm should exist on both sides of the common arm
Linear pair of adjacent angles:
Two lines intersecting at the same point form a linear pair of angles. The angles formed by the intersection of the two lines are said to be adjacent when they coincide. The sum of the linear pair of angles is always 180 degrees.
The angles that share a vertex are the adjacent angles. Thus, the linear pair of angles always have a common vertex. Also, the linear pair has a common arm that represents both angles. A ladder placed against a wall is an example of a linear pair.
The pair of adjacent angles in a linear pair is always constructed on a line segment. However, not all adjacent angles are linear. Therefore, another way of defining a linear pair is the adjacent angle whose non-common arms are the same size.
Difference between vertical & adjacent angles:
- In geometry, it is crucial to be able to distinguish adjacent angles from vertical angles. The easiest way to understand this difference is by imagining two straight lines intersecting each other to form a cross.
- It is equally easy to locate a vertical angle as it is an adjacent angle. Vertical angles have a vertex point in common but do not necessarily share aside.
- A vertical angle is defined as those angles opposite to each other on a cross. For this reason, it is called vertically opposite angles.
Learn more about alternate interior angles with help of Cuemath, your best maths expert.
