Adjacent Angles

Adjacent angles are two angles that share a common vertex and a side, with their other sides lying on the same straight line.

In simpler terms, two angles are adjacent if they are consecutive and their non-shared sides form a straight line.

The sum of two adjacent angles is always equal to a straight angle (180° or π radians).

Thus, adjacent angles are also supplementary angles, and vice versa.

The difference between adjacent and consecutive angles. It's important to note that two adjacent angles are always consecutive. However, the reverse isn't always true: two consecutive angles aren't necessarily adjacent. This is because the sum of two adjacent angles is always 180°, while the sum of two consecutive angles can vary. Both adjacent and consecutive angles share a vertex and a side. The key feature of adjacent angles is that their non-shared sides are aligned. In contrast, for consecutive angles, the non-shared sides might not be aligned.

A Practical Example

Consider two angles:

$$ \alpha = 60° $$

$$ \beta = 120° $$

These two angles share a common vertex and a side, with their other sides aligned on the same straight line.

Therefore, these two angles are adjacent angles.

The sum of the two angles is 180°

$$ \alpha + \beta = 180° $$

And so on.