Maths Library

Calculating Angles: Year 6 maths

This topic covers finding missing angles using fundamental geometric angle facts. The worksheet practises calculating unknown angles on a straight line, around a point, in triangles, and vertically opposite angles.

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What this covers

Calculating Angles is taught in Year 6 (age 11 to 12) as a main teaching focus. It sits in the Geometry strand.

Worked example

Two angles lie on a straight line. One angle is 68 degrees. Find the missing angle x.

  1. Recall that angles on a straight line sum to 180 degrees
  2. Set up the equation: x + 68 = 180
  3. Subtract 68 from 180: x = 112

Answer: 112

Difficulty scale

The sheet generator offers five difficulty settings for this topic.

  1. Complementary angles adding to 90 degrees and supplementary to 180 with two angles
  2. Angles on a straight line or at a point with three angles
  3. Missing angles inside scalene and isosceles triangles
  4. Vertically opposite angles combined with straight line rules
  5. Multi-step problems involving parallel line angle rules (alternate, corresponding)

Common mistakes

  • Assuming angles are equal simply because they look similar rather than applying rules
  • Using 360 degrees instead of 180 degrees for angles on a straight line

Curriculum links

Indicative matches to Australian Curriculum v9. Check wording and codes against the official document.

  • AC9M6SP01 Investigate and calculate combinations of angles on a straight line, at a point, and vertically opposite angles.

Sample sheet and answers

Six questions at the level's usual difficulty. Open the editor to change, add or regenerate any of them.

Calculating Angles

Year 6 maths

Qs
6
Marks
6
NameDateScore / 6
1.
Angles on a straight line add up to 180°. One angle is 71°. Find the other.
[1]
2.
Two angles of a triangle are 79° and 69°. Find the third angle.
[1]
3.
Two angles of a triangle are 51° and 64°. Find the third angle.
[1]
4.
Two angles of a triangle are 75° and 49°. Find the third angle.
[1]
5.
Two angles of a triangle are 46° and 44°. Find the third angle.
[1]
6.
Two angles of a triangle are 38° and 48°. Find the third angle.
[1]

Answer key

  1. 109°180 − 71 = 109
  2. 32°Angles in a triangle add up to 180°; 180 − 79 − 69 = 32
  3. 65°Angles in a triangle add up to 180°; 180 − 51 − 64 = 65
  4. 56°Angles in a triangle add up to 180°; 180 − 75 − 49 = 56
  5. 90°Angles in a triangle add up to 180°; 180 − 46 − 44 = 90
  6. 94°Angles in a triangle add up to 180°; 180 − 38 − 48 = 94