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

Angles in triangles and other shapes

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

  1. Two angles in a triangle are 90° and 30°. What is the third angle?

    • 90°
    • 60°
    • 120°

  2. A regular hexagon has six matching angles, so you can find the size of one angle by dividing the total angle sum by 6.

    Circle one:   True   False

  3. A quadrilateral has three angles of 90°, 90°, and 90°. What is the fourth angle?

    • 180°
    • 90°
    • 80°

  4. A triangle has two angles that measure 55° and 75°. What is the measure of the third angle in degrees?

    Answer: ______________

  5. Two angles of a triangle measure 46° and 59°. Find the measure of the third angle in degrees.

    Answer: ______________

  6. A right triangle has one angle of 90° and another angle of 35°. What is the third angle?

    • 55°
    • 65°
    • 45°
    • 125°

  7. A regular hexagon's six interior angles add up to 720°. What is the size of one interior angle?

    Answer: ______________

  8. An equiangular triangle has all three angles equal. How big is each angle?

    • 60°
    • 90°
    • 45°
    • 120°

  9. A regular pentagon has five equal angles that add up to 540° in total. What is the size of one interior angle?

    Answer: ______________

  10. Ben says: 'Two angles in my triangle are each 80°, so the third one must be 80° too.' What is the third angle really?

    • 80°
    • 160°
    • 20°
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Answer key

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

Angles in triangles and other shapes W1-mt_cdMlC7EpTJ-s1

  1. 60° · 180° - 90° - 30° = 60°. The three angles of a triangle always add up to 180°.
  2. True · Since every angle in a regular hexagon is the same size, splitting the total sum evenly gives you one angle.
  3. 90° · A quadrilateral's angles add up to 360°, not 180°. 360° - 90° - 90° - 90° = 90°.
  4. 50 · The three angles of any triangle add up to 180°, so the missing angle is 180° - 55° - 75° = 50°.
  5. 75 · Since triangle angles sum to 180°, the third angle is 180° - 46° - 59° = 75°.
  6. 55° · Triangle angles add to 180°. With 90° and 35° already used, the last angle is 180 - 90 - 35 = 55°.
  7. 120 · 720° ÷ 6 = 120°. Every angle in a regular hexagon is the same size.
  8. 60° · All equiangular triangles are also equilateral and acute. Since the three equal angles must add to 180°, each one is 180 ÷ 3 = 60°.
  9. 108 · 540° ÷ 5 = 108°. This is the same method used for the hexagon: divide the total by the number of angles.
  10. 20° · 180° - 80° - 80° = 20°. Even when two angles match, all three still have to add up to 180°.
Worksheet · LightMySky