Supplementary Angles Calculator

Enter one angle to find its supplementary angle — the angle that, added to it, sums to 180° — plus a classification of both angles.

Quick Facts

Definition
A + B = 180°
Two angles are supplementary when their measures add to a straight angle.
Supplement formula
B = 180° − A
Subtract the known angle from 180° (or π radians).
Linear pair
Adjacent + supplementary
Two supplementary angles that share a ray and a vertex form a straight line.

Your Results

Calculated
Supplementary Angle
-
B = 180° − A
Sum Check
-
A + B should equal 180°
Angle A Classification
-
Acute, right, or obtuse
Angle B Classification
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Acute, right, or obtuse

Ready

Enter an angle and its unit, then press Calculate.

Formula and Method for Supplementary Angles

Two angles are supplementary when their measures add up to 180° — a straight angle. If you know one angle, you can always find its supplement with a single subtraction: B = 180° − A. This calculator takes your known angle, in degrees or radians, and returns its supplement, confirms the sum equals 180°, and classifies both angles as acute, right, or obtuse.

How the calculation works

Enter the known angle and choose its unit. If you select radians, the calculator first converts the angle to degrees (multiplying by 180/π) so it can apply the supplement formula B = 180° − A, then converts the result back to radians using π/180 if that is the unit you chose. The tool also adds the two angles back together as a sum check (it should always read 180°) and labels each angle acute (less than 90°), right (exactly 90°), or obtuse (greater than 90° and less than 180°).

Common mistakes

  • Confusing supplementary with complementary: supplementary angles sum to 180°; complementary angles sum to only 90°. A 40° angle's supplement is 140°, not 50°.
  • Entering an angle outside the valid range: the known angle must be greater than 0° and less than 180° — otherwise its supplement would be zero or negative, which is not a valid angle.
  • Mixing degrees and radians: make sure the unit selector matches how you measured the angle; 1 radian ≈ 57.3°, so mixing units silently produces a wrong supplement.

Real-world applications

  • Geometry proofs use supplementary angle pairs (like consecutive interior angles cut by a transversal) to establish that lines are parallel.
  • Architecture and carpentry use supplementary angles when two adjacent angles must together form a straight edge, such as roof pitches or mitered corners.
  • Linear pairs — two adjacent supplementary angles formed when a ray splits a straight line — appear constantly in technical drawing and CAD layout.
  • Navigation and surveying use supplementary bearing relationships when a straight reference line is split into two measured angles.

Frequently Asked Questions

What are supplementary angles?
Supplementary angles are two angles whose measures add up to 180°. If one angle measures A, its supplement measures 180° − A.
What is the formula for finding a supplementary angle?
Subtract the known angle from 180°: B = 180° − A (or B = π − A when working in radians). For example, the supplement of 65° is 180° − 65° = 115°.
What is the difference between complementary and supplementary angles?
Complementary angles add up to 90°, while supplementary angles add up to 180°. A 30° angle's complement is 60°, but its supplement is 150°.
Do supplementary angles have to be next to each other?
No. Any two angles that sum to 180° are supplementary, whether or not they touch. When two supplementary angles are adjacent and share a ray, they form a linear pair and their non-shared rays lie on a straight line.

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