Suppose we have two angles α = 50 ⁰ and β = 40 ⁰; If we add them, it gives us 90 ⁰, therefore, we say that α and β “complement each other”, that is, they are **complementary angles**.

**Definition**

The **complementary angles** are those that when added together result in 90⁰ (or π / 2 rad).

α and β are complementary since 62⁰ + 28⁰ = 90⁰

If we have two that are consecutive, the uncommon sides of both form a right angle.

**Complementary angles in a right triangle**

We know that the sum of the interior angles of any triangle is equal to 180⁰. Therefore, in a right triangle the two acute angles are complementary.

α + β = 90⁰

**Trigonometric ratios of complementary angles**

If α and β are complementary (α + β = 90⁰), then β = 90⁰ - α:

**without (90****⁰****-****α) = cos α****cos (90****⁰****-****α) = without α****tg****(90****⁰****-****α) = ctg α****csc****(90****⁰****-****α) = sec α****sec****(90****⁰****-****α) = csc α****ctg (90⁰ - α) = tg α**