Year 9 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.
- 1. The interior angle at A
- 2. The interior angle at B
- 3. The interior angle at C
- 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.Two straight lines cross, making four angles: one at the top, one at the bottom, one on the left and one on the right. Tap the angle vertically opposite the top one.
Write the number of the part.
2.The three angles of a triangle are in the ratio 1 : 2 : 3. How big is the largest, in degrees?
3.Parallel lines are cut by a transversal. Two co-interior angles measure 2x degrees and x degrees. What is x?
4.The exterior angle theorem says an exterior angle of a triangle is equal to...
- a) the largest interior angle
- b) the two interior angles opposite it, added together
- c) the interior angle next to it
- d) half of 180°
5.Two angles form a linear pair. One of them is 118°. What is the other, in degrees?
6.Two straight lines cross. One of the four angles is 47°. What is the angle vertically opposite it, in degrees?
7.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?
8.The proof that vertically opposite angles are equal reaches the line a + b = b + c. What is taken from both sides next?
- a) a
- b) b
- c) 180
- d) c
Answer key — Year 9 Maths — Proving angle facts
- 1. 3 — The bottom angle
- 2. 90
- 3. 60
- 4. b) the two interior angles opposite it, added together
- 5. 62
- 6. 47
- 7. 65
- 8. b) b