Supplementary Angles Calculator

Enter one angle to find its supplementary angle. Two angles are supplementary when they add up to 180 degrees.

Enter an Angle

Result

Supplementary Angle
115
degrees
Given Angle 65
Supplement 115
Sum (Verification) 180
Given in Radians 1.1345
Supplement in Radians 2.0071
Angle Type Acute

Step-by-Step Solution

B = 180 - A = 180 - 65 = 115

What Are Supplementary Angles?

Two angles are supplementary if their measures add up to 180 degrees. When placed adjacent to each other, supplementary angles form a straight line. Each angle is called the supplement of the other. For example, 60 degrees and 120 degrees are supplementary because 60 + 120 = 180.

Angle Pair Types

Supplementary Angles

Two angles that add up to 180 degrees (a straight angle).

A + B = 180

Complementary Angles

Two angles that add up to 90 degrees (a right angle).

A + B = 90

Vertical Angles

Opposite angles formed by two intersecting lines. They are always equal.

A = B

Properties of Supplementary Angles

  • If one angle is acute (less than 90 degrees), its supplement is obtuse (greater than 90 degrees).
  • If one angle is exactly 90 degrees, its supplement is also 90 degrees (both are right angles).
  • Two right angles are always supplementary.
  • Co-interior angles (same-side interior angles) formed by a transversal cutting parallel lines are supplementary.
  • Opposite angles of a cyclic quadrilateral are supplementary.

Real-World Applications

Supplementary angles are used in architecture, engineering, and design. When constructing structures, ensuring that adjacent angles form a straight line (180 degrees) is crucial for alignment. Navigation, astronomy, and surveying also rely on supplementary angle relationships.