Angles & parallel lines · Ages 12–13
Bends and reflex angles
A parallel line through the bend: two alternate angles.
How to do it
Method
A parallel line through the bend: two alternate angles
x = 40° + 35° = 75°, reflex angle = 360° − 75° = 285°
Another way
Extend one side
Alternate angle 35°, exterior angle = 40° + 35° = 75°
In full
Between two parallel lines a path bends at P. One way: draw a line through P parallel to both (a helper line). It splits the angle at P into two parts, each an alternate angle: x = 40° + 35° = 75°. Another: extend AP to meet the other parallel line and use an alternate angle and the exterior angle of the triangle; the answer is the same. Careful: if the angle given is the one beside it (say 140°), turn it into 40° on the straight line first; never add it as it is. For a reflex angle (more than 180°), take it from 360°: 360° − 75° = 285°.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
The two lines are parallel, and the dashed line through the bend is parallel to them. What is x?
- A. 118°
- B. 62°
- C. 242°
- D. 10°
Choose the right answer
Show the answer and working
Answer: A. 118°
The dashed line splits x in two: the upper part = 54°, the lower = 64° (alt. ∠s). x = 54° + 64° = 118°.
Example 2
The two lines are parallel, and the angle at the bend is marked. x =
Show the answer and working
Answer: 31°
A parallel line through the bend splits its angle into two alternate angles: 69° = 38° + x, x = 69° − 38° = 31° (alt. ∠s).
Example 3
The two lines are parallel, and the reflex angle outside the bend is 275°. x =
Show the answer and working
Answer: 34°
The smaller angle at the bend = 360° − 275° = 85° (∠s at a pt.); a parallel line through the bend: 85° = 51° + x, x = 85° − 51° = 34° (alt. ∠s).
Practice questions to try
Try these 5; the answers are at the end. For a whole worksheet, see VIP worksheets below.
1.The two lines are parallel. x =
Answer:
2.The two lines are parallel, and the dashed line through the bend is parallel to them. What is x?
- A. 8°
- B. 104°
- C. 76°
- D. 256°
Choose the right answer
Answer:
3.The two lines are parallel, and the angle at the bend is marked. x =
Answer:
4.The two lines are parallel. The reflex angle x outside the bend = 106°.
True or false?
Answer:
5.The two lines are parallel. The reflex angle x outside the bend =
Answer:
All the answers
- 1. 112°
- 2. B. 104°
- 3. 50°
- 4. False
- 5. 243°
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