Angle sums in triangles and polygons · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Angle sums in triangles and polygons

Mathematics · Geometry · ages 11-14
Name ______________________   Date ____________

  1. One angle of a triangle is 95° and another is 37°. Find the third angle in degrees.

    Answer: ______________

  2. A triangle has angles of 62° and 48°. What is the size of the third angle in degrees?

    Answer: ______________

  3. A triangle has angles of 50° and 70°. What is the third angle?

    • 60°
    • 70°
    • 120°

  4. What do the exterior angles of any polygon always add up to, no matter how many sides it has?

    • 180°
    • 360°
    • 540°

  5. Which regular polygon has an interior angle that is exactly equal to its exterior angle?

    • Equilateral triangle
    • Square
    • Regular hexagon
    • Regular octagon

  6. A regular hexagon has an interior angle sum of 720°. What is each interior angle, since all 6 angles are equal?

    • 100°
    • 120°
    • 140°

  7. The interior angles of a polygon add up to 540°. How many sides does the polygon have?

    Answer: ______________

  8. What is the size of each exterior angle of a regular hexagon, in degrees?

    Answer: ______________

  9. What is the size of each interior angle of a regular pentagon, in degrees?

    Answer: ______________

  10. Zara says an octagon (8 sides) has an angle sum of 8 × 180°, which is 1440°. What did she get wrong?

    • She should have divided by 180° instead of multiplying
    • She should have used 360° instead of 180°
    • She should have used (8 − 2) × 180°, not 8 × 180°
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Answer key

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

Angle sums in triangles and polygons W1-mt_J03RFlVdas-s1

  1. 48 · Subtracting the two known angles from 180° leaves 48° for the third angle.
  2. 70 · The three angles of a triangle always add to 180°, so the missing angle is 70°.
  3. 60° · All three angles add to 180°. 180° minus 50° minus 70° leaves 60°.
  4. 360° · Walk all the way around any polygon and you turn through one full circle: 360°.
  5. Square · A square has interior and exterior angles of 90° each, so they are equal.
  6. 120° · Share the total equally: 720° divided by 6 is 120°.
  7. 5 · A polygon with 540° of interior angles has 5 sides, because 540° is 3 triangles worth of angles.
  8. 60 · The exterior angles of any polygon total 360°, and a regular hexagon shares that equally among 6 corners, giving 60°.
  9. 108 · The angles of a pentagon total 540°, and in a regular pentagon each of the 5 equal angles is 108°.
  10. She should have used (8 − 2) × 180°, not 8 × 180° · Only (n − 2) triangles fit inside the shape, not n. The correct sum is 6 × 180°, which is 1080°.
Worksheet · LightMySky