Maths Library

Calculating Angles: Year 7 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 7 (age 12 to 13) 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.

  • AC9M7SP01 Calculate unknown angles using properties of parallel lines intersected by a transversal and angle sums in polygons.

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 7 maths

Qs
6
Marks
24
NameDateScore / 24
1.
Angles on a straight line add up to 180°. One angle is 71°. Find the other.
[4]
2.
Three angles around a point are 79°, 69° and 148°. Find the fourth angle.
[4]
3.
Find the sum of the interior angles of a polygon with 6 sides.
[4]
4.
Three angles around a point are 75°, 49° and 124°. Find the fourth angle.
[4]
5.
Three angles around a point are 46°, 44° and 90°. Find the fourth angle.
[4]
6.
Find the sum of the interior angles of a polygon with 5 sides.
[4]

Answer key

  1. 109°180 − 71 = 109
  2. 64°Angles around a point add up to 360°; 360 − 79 − 69 − 148
  3. 720°Sum = (n − 2) × 180; (6 − 2) × 180 = 720
  4. 112°Angles around a point add up to 360°; 360 − 75 − 49 − 124
  5. 180°Angles around a point add up to 360°; 360 − 46 − 44 − 90
  6. 540°Sum = (n − 2) × 180; (5 − 2) × 180 = 540