Angles & parallel lines · Ages 12–13
Angles on a line and at a point
180° on a line, 360° round a point.
How to do it
Method
180° on a line, 360° round a point
x + 65° = 180° (adj. ∠s on st. line), x = 115°
Another way
Write an equation
x + x + 100° = 360°, x = 130°
In full
Adjacent angles on a straight line add up to 180° (reason: adj. ∠s on st. line); all the angles round a point add up to 360°, a full turn (reason: ∠s at a pt.). One way: subtract straight away. With 65° and x on a line, x = 180° − 65° = 115°. Another: write an equation. Add all the angles to make 180° or 360°: x + 65° = 180°, then solve. With many angles, or several equal unknowns, the equation is clearer: x + x + 100° = 360°, 2x = 260°, x = 130°. Give the reason with the answer.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
The three angles lie on a straight line. x + 77° + 63° = °, x = °.
Fill in each blank
Show the answer and working
Answer: 180, 40
Angles on a straight line add to 180°: x + 77° + 63° = 180° (adj. ∠s on st. line), x = 180° − 77° − 63° = 40°.
Example 2
Three angles are 114°, 79° and 147°. They can be all the angles round one point.
True or false?
Show the answer and working
Answer: False
All the angles round a point add to 360° (∠s at a pt.). 114° + 79° + 147° = 340°, and it must be 360°.
Example 3
The three angles lie on a straight line, and the two marked x are equal. x =
Show the answer and working
Answer: 72°
x + x + 36° = 180° (adj. ∠s on st. line), 2x = 180° − 36° = 144°, x = 72°.
Practice questions to try
Try these 5; the answers are at the end. For a whole worksheet, see VIP worksheets below.
1.The two angles lie on a straight line. x =
Answer:
2.Which reason finds x in the picture?
- A. adj. ∠s on st. line
- B. ∠s at a pt.
- C. vert. opp. ∠s
- D. ∠ sum of △
Choose the right answer
Answer:
3.The three angles lie on a straight line. x + 36° + 74° = °, x = °.
Fill in each blank
Answer:
4.Two angles are 126° and 54°. They can be adjacent angles on a straight line.
True or false?
Answer:
5.The four angles go round one point, and the three marked x are equal. x =
Answer:
All the answers
- 1. 134°
- 2. A. adj. ∠s on st. line
- 3. 180, 70
- 4. True
- 5. 41°
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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