Supplementary Angles
Find the supplement of any angle instantly with this free online supplementary angles calculator. Two angles are supplementary when they add up to 180 deg, so simply enter your angle to get its supplement. Perfect for students learning trigonometry and angle relationships in geometry, this tool handles angles from 0 deg to 180 deg and shows results with up to 2 decimal places for precision. Use it for homework, lesson planning, or quick reference whenever you need to find a missing supplementary angle in degrees.
About This Calculator
Two angles are supplementary when their measures add up to 180 deg (a straight line). For example, a 60 deg angle and a 120 deg angle are supplementary because 60 deg + 120 deg = 180 deg. Enter any angle and this calculator instantly returns its supplement. The supplement of an angle theta is simply 180 deg - theta. This concept is fundamental in geometry and trigonometry -- for supplementary angles, sin alpha = sin beta while cos alpha = -cos beta. Use this tool to quickly find supplementary angles for geometry problems, trigonometry exercises, or understanding linear pairs and parallel line angle relationships.
Frequently Asked Questions
What are supplementary angles?
Two angles are supplementary when their measures add up to 180 deg, forming a straight line. For example, a 60 deg angle and a 120 deg angle are supplementary because 60 deg + 120 deg = 180 deg. If you have one angle, its supplement is found by subtracting it from 180 deg.
How do you find the supplement of an angle?
To find the supplement of an angle, simply subtract the given angle from 180 degrees. For instance, the supplement of 70 deg is 180 deg - 70 deg = 110 deg. This calculator does this instantly -- just enter your angle and the supplement is displayed immediately.
Can an angle have a supplement if it is greater than 180 deg?
Technically yes, but the supplement would be negative. For example, the supplement of 200 deg is 180 deg - 200 deg = -20 deg. In standard geometry, supplementary angles are typically considered for angles between 0 deg and 180 deg, where both angles are positive.
What is the difference between complementary and supplementary angles?
Complementary angles add up to 90 deg (a right angle), while supplementary angles add up to 180 deg (a straight line). For example, 30 deg and 60 deg are complementary, but 30 deg and 150 deg are supplementary. The complement is found by subtracting from 90 deg, the supplement by subtracting from 180 deg.
What is the relationship between supplementary angles and trigonometry?
For supplementary angles alpha and beta (alpha + beta = 180 deg), the sine of alpha equals the sine of beta (sin alpha = sin beta), while the cosine of alpha is the negative of the cosine of beta (cos alpha = -cos beta). Similarly, tan alpha = -tan beta. This is because supplementary angles share the same reference angle but lie in different quadrants.
Can two obtuse angles be supplementary?
No, two obtuse angles cannot be supplementary. An obtuse angle is greater than 90 deg, so the sum of two obtuse angles would exceed 180 deg. Supplementary angles must consist of either two right angles (both 90 deg) or one acute and one obtuse angle.
Is this tool free?
Yes, all calculators on Calculy are completely free to use with no registration or hidden fees.