Difference Between Angles

The difference between two angles, α and β, is an angle γ such that $$ \alpha - \beta = \gamma $$. When this angle γ is added to angle β, it gives the angle α: $$ \gamma + \beta = \alpha $$.

An Example

Consider two angles measuring 30° and 20°.

$$ \alpha = 30° $$

$$ \beta = 20° $$

The difference between these two angles, α - β, is simply the difference in their measures.

$$ \gamma = \alpha - \beta = 30° - 20° = 10° $$

So, the difference is the angle γ = 10°.

When you add angle γ (the difference) to angle β, you get the measure of angle α.

$$ \gamma + \beta = 10° + 20° = 30° = \alpha $$

Observations

Here are some observations about angle differences:

• If the angles are congruent, meaning they have the same measure, their difference is always zero.
• If I have two pairs of congruent angles, α≅β and γ≅δ, such that α>γ and β>δ, then the differences α-γ and β-δ are also congruent: $$ \alpha - \gamma \cong \beta - \delta $$.

And so on.