Angles & parallel lines · Ages 12–13
Angles with an unknown
Relation first, then the equation; asked for the angle, put x back.
How to do it
Method
Relation first, then the equation; asked for the angle, put x back
3x − 20 = 2x + 10 (vert. opp. ∠s), x = 30
Another way
Check by putting x back
2 × 30 + 10 = 70, 3 × 30 − 20 = 70
In full
When angles are written with x, find how the two are related first, then write the equation: vertically opposite, the two are equal; adjacent on a line, they add to 180°; round a point, all of them add to 360°. Say (2x + 10)° and (3x − 20)° are vertically opposite: 3x − 20 = 2x + 10, x = 30. That isn't the end: if the question asks for the angle, put x back in, 2 × 30 + 10 = 70, so both angles are 70°. Check with the other expression too: 3 × 30 − 20 = 70, the same, so it is right.
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: 20
First the relation: if (4x + 6)° faces 94°, they are equal (vert. opp. ∠s); if side by side, they add to 180° (adj. ∠s on st. line). Here 4x + 6 = 86, 4x = 80, x = 20.
Example 2
The three angles lie on a straight line. x =
Show the answer and working
Answer: 13
(3x + 26) + 2x + 89 = 180 (adj. ∠s on st. line), 5x = 180 − 26 − 89 = 65, x = 13.
Example 3
The two angles lie on a straight line. x = 11.
True or false?
Show the answer and working
Answer: True
(3x + 8) + (4x + 95) = 180 (adj. ∠s on st. line), 7x = 77, x = 11.
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; the two angles written with x are vertically opposite. x =
Answer:
2.The two angles lie on a straight line. x + 5x = 180, x = 180, x = .
Fill in each blank
Answer:
3.The two angles lie on a straight line. x = 29.
True or false?
Answer:
4.Two straight lines cross, as shown. x =
Answer:
5.Two straight lines cross; the two angles written with x are vertically opposite. How many degrees is each of them?
Answer:
All the answers
- 1. 14
- 2. 6, 30
- 3. True
- 4. 17
- 5. 92°
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
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