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Year 7 Maths — Proving angle facts

Use the linear-pair axiom to prove vertically opposite angles equal, and apply the angle-sum and exterior-angle theorems.

Name: ________________________

Before you start

One side of this triangle has been carried straight on past the corner B. Find out what each of the four angles here is called.

1234
  1. 1. The interior angle at A
  2. 2. The interior angle at B
  3. 3. The interior angle at C
  4. 4. The exterior angle at B

The exterior angle at B equals the two interior angles it does not touch — the ones at A and C — added together. That is the exterior angle theorem, and it follows straight from the angle sum.

  1. 1.An exterior angle of a triangle is 110°, and one of the two interior angles opposite it is 45°. What is the other one, in degrees?

  2. 2.The exterior angle theorem says an exterior angle of a triangle is equal to...

    • a) half of 180°
    • b) the largest interior angle
    • c) the two interior angles opposite it, added together
    • d) the interior angle next to it

  3. 3.Two angles of a triangle are 55° and 65°. What is the third, in degrees?

  4. 4.Parallel lines are cut by a transversal, and one of a pair of alternate interior angles is 73°. What is the other, in degrees?

  5. 5.Sort each set of angles by whether they must be equal or must add up to 180°.

    Groups: Must be equal · Must add up to 180°

    • Alternate interior angles on parallel lines
    • Co-interior angles on parallel lines
    • Corresponding angles on parallel lines
    • Vertically opposite angles
    • A linear pair
    • The three angles of a triangle

  6. 6.Parallel lines are cut by a transversal. Two co-interior angles measure 2x degrees and x degrees. What is x?

  7. 7.Two angles form a linear pair. One of them is 118°. What is the other, in degrees?

  8. 8.Two straight lines cross. One of the four angles is 47°. What is the angle vertically opposite it, in degrees?

Answer key — Year 7 Maths — Proving angle facts

  1. 1. 65
  2. 2. c) the two interior angles opposite it, added together
  3. 3. 60
  4. 4. 73
  5. 5. Vertically opposite angles → Must be equal; A linear pair → Must add up to 180°; Alternate interior angles on parallel lines → Must be equal; Co-interior angles on parallel lines → Must add up to 180°; Corresponding angles on parallel lines → Must be equal; The three angles of a triangle → Must add up to 180°
  6. 6. 60
  7. 7. 62
  8. 8. 47