Angles & parallel lines · Ages 12–13
Angles with parallel lines
Parallel: corr. and alt. equal, int. add to 180°.
How to do it
Method
Parallel: corr. and alt. equal, int. add to 180°
∠EFD = ∠AEF = 65° (alt. ∠s, AB // CD)
Another way
In two steps
Vert. opp. ∠s first, then corr. ∠s
In full
When two lines are parallel: corresponding angles are equal (reason: corr. ∠s, AB // CD); alternate angles are equal (reason: alt. ∠s, AB // CD); interior angles on the same side add up to 180° (reason: int. ∠s, AB // CD). So the eight angles a transversal makes have only two sizes: a, and 180° − a. One way: find one relation that goes straight there. Another: two steps, first a vertically opposite angle or a straight line, then the parallel lines. The answers agree; give a reason for every step.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
In the picture AB // CD. x =
Show the answer and working
Answer: 75°
Place first: corresponding (F) and alternate (Z) angles are equal, interior ones (C) add to 180° (AB // CD). Where x is from 105° gives x = 75°.
Example 2
In the picture AB // CD. x = 130° (______). Which reason goes in the blank?
- A. int. ∠s, AB // CD
- B. corr. ∠s, AB // CD
- C. alt. ∠s, AB // CD
- D. vert. opp. ∠s
Choose the right answer
Show the answer and working
Answer: C. alt. ∠s, AB // CD
x and 130° are on opposite sides, both between AB and CD (a Z): alternate angles. AB // CD, so x = 130° (alt. ∠s, AB // CD).
Example 3
In the picture AB // CD. x =
Show the answer and working
Answer: 33
The two are on opposite sides, both between AB and CD: alternate angles, so equal. 3x + 16 = 4x − 17 (alt. ∠s, AB // CD), x = 33, x = 33.
Practice questions to try
Try these 5; the answers are at the end. For a whole worksheet, see VIP worksheets below.
1.In the picture AB // CD. x =
Answer:
2.In the picture AB // CD. x = °, y = °, z = °.
Fill in each blank
Answer:
3.In the picture AB // CD. x =
Answer:
4.In the picture AB // CD. x =
Answer:
5.In the picture AB // CD. x =
Answer:
All the answers
- 1. 125°
- 2. 40, 40, 140
- 3. 45°
- 4. 26
- 5. 130°
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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