Basic Geometry • Topic 2 of 3

Pairs of Angles: Complementary & Supplementary

What are complementary and supplementary angles? When we look at pairs of angles, we often find special relationships based on what their measures add up to.

Complementary Angles: Two angles are called complementary if the sum of their measures is exactly \(90^\circ\). If you put them side-by-side, they form a perfect right angle (\(L\)-shape). Think of the letter 'C' in Complementary stands for "Corner" (a \(90^\circ\) corner).

  • Formula: \(\angle A + \angle B = 90^\circ\)
  • Example: Angles measuring \(40^\circ\) and \(50^\circ\) are complementary because \(40^\circ + 50^\circ = 90^\circ\). We say that \(40^\circ\) is the complement of \(50^\circ\).

Supplementary Angles: Two angles are called supplementary if the sum of their measures is exactly \(180^\circ\). When placed together, they form a flat, straight line. Think of the letter 'S' in Supplementary stands for "Straight line" (\(180^\circ\) line).

  • Formula: \(\angle A + \angle B = 180^\circ\)
  • Example: Angles measuring \(110^\circ\) and \(70^\circ\) are supplementary because \(110^\circ + 70^\circ = 180^\circ\). We say that \(110^\circ\) is the supplement of \(70^\circ\).
Angle RelationshipSum of MeasuresVisual Shape Formed
Complementary\(90^\circ\)Right Angle (Corner)
Supplementary\(180^\circ\)Straight Line
Types of Lines & AnglesParallel LinesIntersectingPerpendicularAcute < 90°Right = 90°Obtuse 90°-180°Straight = 180°Reflex > 180°
Solved Examples
1
Worked Example
Find the complement of an angle that measures \(38^\circ\).
Solution*Step 1: Remember that complementary angles add up to \(90^\circ\). *Step 2: Let the unknown complement angle be \(x\). *Step 3: Set up the equation: \(x + 38^\circ = 90^\circ\). *Step 4: Subtract \(38^\circ\) from \(90^\circ\): \(x = 90^\circ - 38^\circ = 52^\circ\).

Key Points

  • Complementary angles have a sum of exactly \(90^\circ\).
  • Supplementary angles have a sum of exactly \(180^\circ\).
  • To find the complement of an angle, subtract its measure from \(90^\circ\).
  • To find the supplement of an angle, subtract its measure from \(180^\circ\).
  • Complementary angles form an L-shape; supplementary angles form a straight line.
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Quick Check — 4 MCQs
Tap an option to check your answer0 / 4
Q1.Two angles are complementary if they sum to:
Explanation: $90^\circ$.
Q2.Two angles are supplementary if they sum to:
Explanation: $180^\circ$.
Q3.The complement of $40^\circ$ is:
Explanation: $90-40$.
Q4.The supplement of $110^\circ$ is:
Explanation: $180-110$.
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