Adjacent Angles
Adjacent angles can be defined as two angles with a common vertex and a common side. Adjacent angles can either be complementary or supplementary angles when they share a common vertex or side.
Here, \(\angle{AOC}\) and \(\angle{BOC}\) are adjacent angles as they share a common vertex (O) and a common side (OC).
Examples of Adjacent Angles
A few examples of adjacent angles are given below:
- If a line is drawn on a straight line, the supplementary angles will be adjacent angles.
- A real-life example of adjacent angles can be given by the steering wheel of a vehicle.
Properties of Adjacent Angles
Here are some of the important properties of adjacent angles:
- They share a common vertex.
- They share a common side.
- Both angles do not overlap each other.
- Angles can be complementary or supplementary, but they don’t have to be.
Solved Examples
Example 1:
Identify whether angle 1 and angle 2 are adjacent angles based on the following diagram.
Solution:
In the above figure, we can see that angles 1 and 2 share a common vertex, O, and a common side, OB. Thus, the angles are adjacent angles.
Example 2:
Megan bought a pizza for a party at her home. By the end of the night, she noticed that two pizza slices were lying next to each other in the following way.
Do the edges of the slices form adjacent angles?
Solution:
As we can see from the image, the pizza slices are lying next to each other, and hence they have a common vertex and a common side. Thus the pizza slices are forming adjacent angles.
Example 3:
From the following figure, can you identify if angles 1 and 2 are adjacent or not?
Solution:
We can see that angle 1 doesn’t have a common vertex with angle 2. As a result, angle 1 and angle 2 are not adjacent angles.
Example 4:
From the following figure, find the angle \(\alpha\).
Solution:
As we know, one of the properties of adjacent angles is that the sum of adjacent angles can be complementary.
From the above figure, we can see that both the angles share a common vertex and common side. Hence, they are adjacent angles. Now, their summation will give us 90° as they are complementary.
Hence, 30° + \(\alpha\) = 90°
\(\alpha\) = 90° – 30° = 60°
Thus, the measure of angle \(\alpha\) is 60°.
Vertical angles are those angles that lie opposite to each other. Hence, they cannot be adjacent angles as adjacent angles lie next to each other.
Adjacent angles can be added together. The sum of two angles can be either complementary, or supplementary, or it can give any other value, based on their measurements.
No, adjacent angles cannot overlap each other.
Yes, for two angles to be adjacent angles, they should have a common side.