Complementary & Supplementary Angles Worksheet + PDF

Complementary & Supplementary Angles Worksheet 📐 Free PDF + Answer Key

✍ Written & fact-checked by Dr. Irfan Mansuri  |  Last Updated: July 2026

Imagine you’re helping a friend hang a picture frame on the wall. You tilt it slightly and notice the angle between the frame and the wall — and the angle between the frame and the ceiling. Those two angles together form a perfect straight line: 180°. That’s a supplementary pair, right there in your living room. 🏠

Complementary and supplementary angles are one of the most tested angle-relationship concepts in middle school geometry. Complementary angles add up to 90°, supplementary angles add up to 180°, and finding a missing angle in either pair takes exactly one subtraction step. This worksheet gives you a full lesson plus 10 graded practice problems to master both.

In this guide, you get a real lesson first — not just a list of definitions — followed by a printable PDF worksheet with a full answer key. By the end, you’ll be able to solve any complementary or supplementary angle problem, including the algebraic ones that trip up most students.

• 🎯 Understand the difference between complementary and supplementary angles
• 🔢 Find missing angles using subtraction and simple algebra
• 🖨️ Download and print a 10-problem worksheet with a full answer key
• ❌ Avoid the three most common mistakes students make on tests

🌍 Where You See These Angles in Real Life

Complementary and supplementary angles appear everywhere once you start looking. Architects use them to design staircases — a staircase tread and riser form a complementary pair that must sum to exactly 90° for the step to be level. 🏗️

A door hinge opens to form a supplementary pair with the wall: when the door is fully open against the wall, the door and the wall together make a 180° straight line. Carpenters check this constantly. A clock face is another great example: at 3:00, the minute and hour hands form a 90° complementary angle. At 6:00, they form a 180° supplementary (straight) angle.

In sports, a basketball backboard meets the floor at 90°. The angle of a soccer ball’s trajectory off a wall and the angle of incidence are supplementary. Even in graphic design, rotating an element by its supplementary angle flips it to the mirror position on a straight line.

📐 Visual Diagram: Complementary vs Supplementary

The diagram below shows both angle types side by side. Study it before reading the definitions — your brain will absorb the rule faster with a visual anchor. 👇

  COMPLEMENTARY ANGLES                SUPPLEMENTARY ANGLES
  ─────────────────────               ──────────────────────────────

         │  ↖ 55°                     ←─────────────────────────────→
         │ /                           straight line (180°)
    35°  │/                           ──────────────┬───────────────
  ───────┘                                  110°    │   70°
   right angle = 90°                               (point on line)

  35° + 55° = 90° ✅                  110° + 70° = 180° ✅

  Both angles MUST be acute.          One angle CAN be obtuse.
  (each < 90°)                        (as long as sum = 180°)

  Memory: C = Corner = 90°            Memory: S = Straight = 180°

📖 What Are Complementary and Supplementary Angles?

A complementary angle pair is any two angles whose measures add up to exactly 90°. The angles do not need to be adjacent (touching) — they just need to sum to 90°. For example, 20° and 70° are complementary even if they are drawn on opposite sides of a page.

A supplementary angle pair is any two angles whose measures add up to exactly 180°. When supplementary angles are adjacent and share a common vertex, they form a straight line — this is called a linear pair. But again, they don’t have to be adjacent to be supplementary.

One definition that trips up students: complementary and supplementary describe a relationship between two angles, not a property of one angle alone. You cannot say “this angle is complementary” without naming what it is complementary to.

🔢 How to Find a Missing Angle: Step-by-Step

Finding a missing angle in a complementary or supplementary pair takes exactly four steps. Follow this process every time and you will never mix them up. ✅

1. Identify the relationship. Read the problem carefully. Does it say “complementary” (sum = 90°) or “supplementary” (sum = 180°)? If neither word appears, look for a right-angle symbol (□) for complementary, or a straight line for supplementary.
2. Write the equation. Let the missing angle = x. Write: known angle + x = 90° (complementary) or known angle + x = 180° (supplementary).
3. Solve for x. Subtract the known angle from 90° or 180°. If the problem uses expressions like (2x + 10)°, combine like terms first, then solve.
4. Check your answer. Add both angles together. The sum must equal exactly 90° or 180°. If it doesn’t, recheck your arithmetic.

🔍 Worked Example 1 — Basic Subtraction

🔍 Worked Example 2 — Algebraic Expression

🔍 Worked Example 3 — Word Problem

❌ Common Mistakes Students Make (and How to Fix Them)

These three errors appear constantly in student work. Recognising them now saves you marks on every geometry test. 🚨

🖊️ On-Page Practice Worksheet — 10 Problems

Work through all 10 problems below. They start with simple subtraction and build up to algebraic and word-problem types — the same progression used in classroom assessments. Use the Answer Key to self-check when you’re done. 📝

Instructions: Find the missing angle in each problem. State whether the angle pair is complementary (sum = 90°) or supplementary (sum = 180°), then solve. Show your working.

1. Angles A and B are complementary. Angle A = 30°. Find angle B.
2. Angles P and Q are supplementary. Angle P = 120°. Find angle Q.
3. Two complementary angles are equal. Find each angle.
4. Angles X and Y are supplementary. Angle X = 3 × angle Y. Find both angles.
5. Find the complement of 67°.
6. Find the supplement of 43°.
7. Angles M and N are complementary. Angle M = (2x + 10)° and angle N = (3x)°. Find x and both angles.
8. Angles C and D are supplementary. Angle C = (5x − 20)° and angle D = (3x + 8)°. Find x and both angles.
9. An angle is 18° more than its complement. Find both angles.
10. An angle is 40° less than three times its supplement. Find the angle.

How to use this worksheet: Print the PDF (or use the on-page version above). Cover the Answer Key section and attempt all 10 problems. Then reveal the key and check each answer. For any problem you got wrong, re-read the relevant worked example above and try a similar problem before moving on.