Supplementary angles are pairs of angle

Angle

In geometry, an angle is the figure formed by two rays sharing a common endpoint, called the vertex of the angle.Angles are usually presumed to be in a Euclidean plane with the circle taken for standard with regard to direction. In fact, an angle is frequently viewed as a measure of an circular arc...

s that add up to 180 degrees

Degree (angle)

A degree , usually denoted by ° , is a measurement of plane angle, representing 1⁄360 of a full rotation; one degree is equivalent to π/180 radians...

. Thus the supplement of an angle of x degrees is an angle of (180 − x) degrees.

If the two supplementary angles are adjacent

Adjacent angles

In geometry, adjacent angles, often shortened as adj. ∠s, are angles that have a common ray coming out of the vertex going between two other rays. In other words, they are angles that are side by side, or adjacent.- Complementary adjacent angles :...

 (i.e. have a common vertex

Vertex (geometry)

In geometry, a vertex is a special kind of point that describes the corners or intersections of geometric shapes.-Of an angle:...

 and share just one side), their non-shared sides form a straight line

Line (geometry)

The notion of line or straight line was introduced by the ancient mathematicians to represent straight objects with negligible width and depth. Lines are an idealization of such objects...

. However, supplementary angles do not have to be on the same line, and can be separated in space. For example, adjacent angles of a parallelogram

Parallelogram

In Euclidean geometry, a parallelogram is a convex quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure...

 are supplementary, and opposite angles of a cyclic quadrilateral

Cyclic quadrilateral

In Euclidean geometry, a cyclic quadrilateral is a quadrilateral whose vertices all lie on a single circle. This circle is called the circumcircle or circumscribed circle, and the vertices are said to be concyclic. Other names for these quadrilaterals are chordal quadrilateral and inscribed...

 (one whose vertices all fall on a single circle) are supplementary.

Trigonometric ratios

The sine

Sine

In mathematics, the sine function is a function of an angle. In a right triangle, sine gives the ratio of the length of the side opposite to an angle to the length of the hypotenuse.Sine is usually listed first amongst the trigonometric functions....

s of supplementary angles are equal. Their cosines and tangent

Tangent

In geometry, the tangent line to a plane curve at a given point is the straight line that "just touches" the curve at that point. More precisely, a straight line is said to be a tangent of a curve at a point on the curve if the line passes through the point on the curve and has slope where f...

s (unless undefined) are equal in magnitude but have opposite signs.

External links

• Animated demonstration - Interactive applet and explanation of the characteristics of supplementary angles.
• Angle definition pages with interactive applets that are also useful in a classroom setting. Math Open Reference