Supplementary angles are two angles whose measures add up to 180 degrees. Each one is the supplement of the other, so the supplement of an angle x is 180° − x. When they share a side, they form a straight line, called a linear pair. For example, 118° and 62° are supplementary.
Supplementary means the two measures total 180°. When the angles sit side by side they make a straight line; apart, they still count.
Formal definition and notation
Two angles ∠ A and ∠ B are supplementary if and only if m∠ A + m∠ B = 180°. They need not be adjacent. If they are adjacent and their outer sides are opposite rays, they form a linear pair, and every linear pair is supplementary. The term always describes a pair, not a single angle.
Symbol
Read it as
Meaning
m∠ A + m∠ B = 180°
the measure of angle A plus the measure of angle B equals 180 degrees
the test for a supplementary pair
Key facts
Angles that form a straight line (a linear pair) are always supplementary. This is the fact used most often to find missing angles.
Two right angles are supplementary: 90° + 90° = 180°.
Complementary angles add to 90°. The angle 50° has supplement 130° and complement 40°.
Supplementary Anglesvs.Linear pair
A linear pair is two adjacent angles that form a line. Every linear pair is supplementary, but supplementary angles do not have to be adjacent.
Quick check: 3 questions
Question 1 of 3
What is the supplement of 129°?
Show answer and explanation
Answer: A.180° − 129° = 51°. 231° subtracts from 360, 61° is a borrowing slip, and 39° is 129 − 90, which mixes in the right angle.
Question 2 of 3
Two supplementary angles are equal. What does each measure?
Show answer and explanation
Answer: C.x + x = 180 gives x = 90. 45° halves 90 (the complementary total), 60° splits 180 into three parts, and 180° forgets to divide.
Question 3 of 3
A ray splits a straight angle so that one angle is 4 times the other. What is the larger angle?
Show answer and explanation
Answer: D.x + 4x = 180, so x = 36 and the larger angle is 4 × 36 = 144°. 36° is the smaller angle, 72° uses 90 as the total, and 120° treats 4 times as 2 times.
Supplementary Angles: frequently asked questions
Do supplementary angles have to be adjacent?
No. Any two angles whose measures total 180° are supplementary, even if they are in different figures. When supplementary angles are adjacent and form a straight line, they are called a linear pair. Problems use linear pairs most often, because a straight line in a diagram tells you the two angles add to 180°.
Can three angles be supplementary?
Not by the usual definition. Supplementary describes exactly two angles that add to 180°. Three angles can still add to 180°, as the angles of every triangle do, or as three angles along a straight line do, but you would say they sum to 180° rather than call them supplementary.
What is the difference between supplementary and complementary angles?
The total. Supplementary angles add to 180° and form a straight line when placed side by side. Complementary angles add to 90° and form a right angle. So 70° has supplement 110° and complement 20°. Remember: C before S, 90 before 180.
Updated November 2026·Reviewed by the Effortless Math team·Standards: CCSS 7.G.B.5
Cite this entry
Effortless Math Team. “Supplementary Angles.” Effortless Math Dictionary. Updated November 2026. https://www.effortlessmath.com/math-dictionary/supplementary-angles/
Flashcard
TermSupplementary Anglestwo angles, total 180°
DefinitionTwo angles whose measures add to 180°. The supplement of x is 180° − x: 130° and 50° are supplementary.
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