Angles that add up on a diagram · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Finding a Missing Angle

Mathematics · Geometry · ages 9-10
Name ______________________   Date ____________

  1. Two angles sit on a straight line, exactly filling it. How many degrees do they add up to together?

    • 90° (a quarter turn)
    • 360° (one full turn)
    • 180° (half a turn)

  2. An angle is split into exactly two parts. If you know the whole angle and one part, you can subtract to find the missing part.

    Circle one:   True   False

  3. Two angles sit on a straight line, exactly filling it. One angle is 25°, the other is x°. What is x?

    • 165°
    • 155°
    • 205°

  4. An angle of 150° is split into two parts that exactly fill it with no gaps or overlaps. One part is 60°. Which operation finds the other part?

    • Add 60 and 150
    • Subtract 60 from 150
    • Subtract 60 from 180

  5. An angle is split into two parts that exactly fill it with no gaps or overlaps. One part is 42°. The whole angle is 110°. What is the other part?

    Answer: ______________

  6. Two angles on a straight line, exactly filling it, are 75° and x°. Which equation finds x?

    • 75 + x = 180
    • 75 + x = 360
    • x = 75 + 180

  7. An angle is split into two parts. One part is 28°. The whole angle is 90°. What is the other part?

    Wholeangle90Known part28

    Answer: ______________

  8. An angle is split into two parts. The whole angle is 115° and one part is 45°. What is the other part?

    Wholeangle115Known part45
    • 45°
    • 160°
    • 70°

  9. Four angles are arranged around a point and fill one full turn with no gaps or overlaps. Three of them measure 100°, 85°, and 95°. What is the fourth angle, x?

    100°10085°8595°95

    Answer: ______________

  10. Three angles sit around a point, filling one full turn with no gaps or overlaps: 60°, 70°, and x°. Mia writes 60 + 70 + x = 180 and gets x = 50°. What mistake did Mia make?

    • She added 60 and 70 incorrectly
    • She forgot to name the missing angle x
    • She used the straight-line total instead of the point total
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Answer key

For grown-ups. Fold this page away before handing over the rest.

Finding a Missing Angle W1-mt_89riIKwGYp-s1

  1. 180° (half a turn) · A straight line is half of a full turn, so angles on it always add up to 180°.
  2. True · Whole = part + part, so missing part = whole minus known part.
  3. 155° · 25 + x = 180, so x = 180 - 25 = 155°.
  4. Subtract 60 from 150 · The given whole is 150°, not 90, 180 or 360. Subtract the known part from the given whole: 150 - 60 = 90.
  5. 68 · The two parts exactly fill the whole angle of 110°. Subtract 42 from 110 to get 68.
  6. 75 + x = 180 · Angles exactly filling a straight angle total 180°, so the equation is 75 + x = 180.
  7. 62 · The two parts must add to the whole: 28 + x = 90, so x = 62°.
  8. 70° · The two parts must add to the whole: 45 + x = 115, so x = 70°.
  9. 80 · Angles exactly filling one full turn add to 360°. 100 + 85 + 95 + x = 360, so x = 80°.
  10. She used the straight-line total instead of the point total · Angles exactly filling one full turn total 360°, not 180°. The right equation is 60 + 70 + x = 360, so x = 230°.
Worksheet · LightMySky