# Difference Between Complementary and Supplementary Angles: Complementary vs Supplementary Angles

Complementary vs Supplementary Angles

Geometry, a pillar of mathematics, is one of the oldest forms of mathematics. Geometry is the branch of mathematics which study the shapes and size of the figures and space. The basic concepts of geometry in the present day mathematical form were developed by the ancient Greeks. The development culminated in “The Elements”, the timeless and renowned book by the great mathematician Euclid, who is often considered as the “Father of Geometry”. The principles of geometry stated by Euclid 2500 years ago are true today too.

What is Complementary Angle?

The study of angles is important in geometry, and the special cases arising are given identical names for reference. Two angles are said to be complementary when their sum is equal to 900. In other words, it can be said that together they form a right angle.

Following theorems consider the complementary angles.

• Complements of the same angle are congruent. In simple, if two angles are complement to a third angle, the first two angles are equal in size.

• Complements of congruent angles are congruent. Consider two angles that are equal in size. The complementary angles of these angles are equal to each other.

Also in trigonometric ratios, the prefix “co” comes from the complementary. In fact, cosine of an angle is the sine of its complementary angle. Likewise, “co”tangent and “co”secant are also the values of the complementary.

What is Supplementary Angle?

Two angles are said to be supplementary when their sum is 1800. In another way, two angles residing on any point of the straight line (only two angles) are supplementary. That is, if both are adjacent and share a common side (or a vertex), the other sides of the angles coincide with a straight line.

Following are two theorems that consider supplementary angles

• Adjacent angles of a parallelogram are supplementary

• Opposite angles of a cyclic quadrilateral are supplementary

What is the difference between Complementary and Supplementary Angles?