Angles & parallel lines · Ages 12–13
Vertically opposite angles
Opposite angles equal; angles side by side add to 180°.
How to do it
Method
Opposite angles equal; angles side by side add to 180°
One angle 70°: the opposite one 70°, the next one 110°
Another way
By angles on a line
a + b = 180°, b + c = 180°, so a = c
In full
Two crossing lines make four angles; the two facing each other are vertically opposite, and they are equal (reason: vert. opp. ∠s). Why? Each makes a straight line with the same angle between them: a + b = 180° and b + c = 180°, so a = c. Angles side by side add up to 180°. So if one angle is 70°, the four are 70°, 110°, 70°, 110°. Where three lines meet at a point, find the opposite angles first, bring the angles onto one straight line, then use 180°.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
Two straight lines cross, as shown. x =
Show the answer and working
Answer: 68°
x faces 68° across the crossing, so they are vertically opposite: x = 68° (vert. opp. ∠s).
Example 2
Two straight lines cross, as shown. Which statement is right?
- A. x = 40° (vert. opp. ∠s)
- B. x = 140° (adj. ∠s on st. line)
- C. x = 40° (adj. ∠s on st. line)
- D. x = 140° (vert. opp. ∠s)
Choose the right answer
Show the answer and working
Answer: C. x = 40° (adj. ∠s on st. line)
Two angles facing each other are vertically opposite and equal; two side by side lie on a straight line and add to 180°. Here x = 40°.
Example 3
Three straight lines meet at a point, as shown. x =
Show the answer and working
Answer: 73°
The angle opposite 36° lies on one straight line with 71° and x: x = 180° − 36° − 71° = 73° (vert. opp. ∠s, adj. ∠s on st. line).
Practice questions to try
Try these 5; the answers are at the end. For a whole worksheet, see VIP worksheets below.
1.Two straight lines cross, as shown. x =
Answer:
2.Two straight lines cross, as shown. Which statement is right?
- A. x = 127° (vert. opp. ∠s)
- B. x = 127° (adj. ∠s on st. line)
- C. x = 53° (adj. ∠s on st. line)
- D. x = 53° (vert. opp. ∠s)
Choose the right answer
Answer:
3.Three straight lines meet at a point, as shown. x =
Answer:
4.Two straight lines cross, as shown, and the two angles marked a add up to 138°. x =
Answer:
5.Two straight lines cross, and a ray splits one of the angles into two equal angles x, as shown. x =
Answer:
All the answers
- 1. 41°
- 2. D. x = 53° (vert. opp. ∠s)
- 3. 52°
- 4. 111°
- 5. 47°
VIP practice notes and papers
Aimed at tests and exams: questions on this topic, new every time, to print or save as a PDF.
- Practice notes: The key point, worked examples step by step, then questions of the same kind to follow, hints fading
- Practice paper: Set out in parts like a school paper, marked, with answers and full working
Start playingPlay and learn in the secondary world, Star Galaxy: animated methods, monster battles, a review of every mistake