Maths Library

Finding Angle Measures: Grade 7 math

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

Finding Angle Measures is taught in Grade 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 Common Core State Standards. Check wording and codes against the official document.

  • 7.G.B.5 Use facts about supplementary, complementary, vertical, and adjacent angles to write and solve simple equations.

Sample sheet and answers

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

Finding Angle Measures

Grade 7 math

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