Understanding angles (age 10+) · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Angles at a point, on a line, and across a cross

Mathematics · Geometry · ages 10-11
Name ______________________   Date ____________

  1. Two straight lines cross. One opening is 65°. What is the opening vertically opposite to it?

    Answer: ______________

  2. Two straight lines cross. Which pair of measures could be the vertically opposite angles?

    • 40° and 40°
    • 50° and 60°
    • 70° and 80°

  3. Angles meet at a single point and fill all the space around it with no gaps or overlaps. What do they add up to?

    • 360°
    • 90°
    • 180°

  4. When two straight lines cross, the angles opposite each other are called vertically opposite angles and they are always equal.

    Circle one:   True   False

  5. A straight angle is split into three parts that exactly fill it with no gaps or overlaps. Two parts are 50° and 60°. What is the third part?

    Answer: ______________

  6. Two straight lines cross at a point. One angle is 48°. What is the size of the angle vertically opposite to it?

    • 42°
    • 132°
    • 48°

  7. Three angles fill one full turn with no gaps or overlaps. Two are 100° and 120°. A third is proposed as 140°. Which equation checks it?

    • 100 + 120 = 140
    • 100 + 120 + 140 = 360
    • 360 + 100 = 120 + 140

  8. Two straight lines cross at right angles. One opening is 90°. The opening next to it is also 90°.

    Circle one:   True   False

  9. At a point, three angles measure 95°, 130°, and 145°. Zara says these three angles exactly fill the space around the point with no gaps or overlaps. Is she right?

    • No, they add up to more than 360°
    • Yes, they add up to exactly 360°
    • No, they add up to less than 360°

  10. Two straight lines cross. One angle is 40°. The neighbouring angle is split into two equal parts. What is each part?

    • 70°
    • 140°
    • 20°
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Answer key

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

Angles at a point, on a line, and across a cross W1-mt_QDTO3GAgcq-s1

  1. 65 · Vertically opposite angles are equal, so the opposite opening is also 65°.
  2. 40° and 40° · Vertically opposite angles are always equal. Only 40° and 40° are equal.
  3. 360° · Angles filling all the space around one point make a full turn, which is 360°.
  4. True · Vertically opposite angles share the same vertex but no ray. They are always equal.
  5. 70 · Add the two known parts: 50 + 60 = 110. Subtract from 180: 180 - 110 = 70.
  6. 48° · Vertically opposite angles are equal, so the opposite angle is also 48°.
  7. 100 + 120 + 140 = 360 · Add all three parts: 100 + 120 + 140 = 360. The total matches one full turn.
  8. True · At a perpendicular crossing, all four openings are 90°. Adjacent openings exactly fill a straight angle: 90 + 90 = 180.
  9. No, they add up to more than 360° · 95 + 130 + 145 = 370, which is 10 more than 360. Three angles exactly filling one full turn must total exactly 360.
  10. 70° · The neighbouring angle is 180 - 40 = 140. Split equally: 140 / 2 = 70.
Worksheet · LightMySky