Angles at a point, on a line and in parallel lines
Angle rules are like a set of keys — once you know which one fits, missing angles unlock in seconds.
Part of your national curriculum
- Geometry and measures: Apply the properties of angles at a point, on a straight line, vertically opposite angles, and angles in parallel lines
Lesson overview
What you'll learn in this lesson
Apply the properties of angles at a point, on a straight line, vertically opposite angles, and angles in parallel lines
Key learning points
- • The core rules
- • Worked example
- • Parallel lines example
This lesson at a glance
- 24 minutes
- 14 parts to scroll through
- 3 quick checks
- Marked quiz at the end
- Gentle pace: short sittings with pauses
Words to know
Scroll down — the lesson carries on below
Watch & discover
Part 1 of 14
Watch first
Angles at a point, on a line and in parallel lines
An English teaching video on this topic from Homeschool Pop. Watch it, then scroll down for the lesson.
In a nutshell
Apply the properties of angles at a point, on a straight line, vertically opposite angles, and angles in parallel lines
Learning cycle
Part 2 of 14
Learning cycle 1 of 2
Part 1 · The core rules
A short piece of teaching, then a check to make sure it has landed.
Explore the idea
Part 3 of 14
Learn
The core rules
Angles on a straight line sum to 180°. Angles around a point sum to 360°. Vertically opposite angles (formed by two crossing lines) are equal. Angles in parallel lines cut by a transversal give equal alternate and corresponding angles.
Explore the idea
Part 4 of 14
Learn
Worked example
Two angles on a straight line are x and 65°. Since they sum to 180°: x = 180 - 65 = 115°.
Quick check
Part 5 of 14
Quick check
Two angles on a straight line are x and 65°. What is x?
Reset break
Part 6 of 14
Pause
That's sitting 1 of 2 done
Stretch, get a drink, look out of the window. There is no timer and nothing is counting down — your place is saved, so you can come back in five minutes or tomorrow.
Quick check
Part 7 of 14
Quick check
Angles around a point sum to how many degrees?
Learning cycle
Part 8 of 14
Learning cycle 2 of 2
Part 2 · Parallel lines example
A short piece of teaching, then a check to make sure it has landed.
Explore the idea
Part 9 of 14
Learn
Parallel lines example
A transversal crosses two parallel lines, making a corresponding angle of 72° with the first line. The corresponding angle at the second line is also 72°, since corresponding angles are equal.
Quick check
Part 10 of 14
Quick check
If a corresponding angle is 72°, what is the matching corresponding angle on the other parallel line?
Challenge round
Part 11 of 14
Game · Sort it
Which of these are true?
Drag each card into the right column. Tap a card first if dragging is fiddly.
True
Not true
Challenge round
Part 12 of 14
Game · Fill the gaps
Finish the sentences
Choose the word that belongs in each gap.
____ on a straight line sum to 180°.
____ opposite angles (formed by two crossing lines) are equal.
Two angles on a ____ line are x and 65°.
Mastery quiz
Part 13 of 14
Marked quiz
End of lesson quiz: Angles at a point, on a line and in parallel lines
3 questions, marked with the reasoning shown. No timer.
1. Two angles on a straight line are x and 65°. What is x?
2. Angles around a point sum to how many degrees?
3. If a corresponding angle is 72°, what is the matching corresponding angle on the other parallel line?
Lesson round-up
Part 14 of 14
Lesson round-up
Ready when you are
Quiz score
Not sat
Games
Not played
Points this lesson
0
Best run
0 in a row
Luna: 0 out of 3 on the practice checks. Only if you feel up to it — one more?
Ask LunaDo the work
Your written work for this lesson
This is the part you'd do in your book at school. Pick the pieces below, write here or on paper, and photograph anything you draw or work out.
The cost of a school trip
A school is planning a trip to a wildlife park. The coach costs £480 however many people go. Entry costs £9.50 for each pupil and each adult goes free. The school says every pupil must pay the same amount, and the trip must not lose money.
If 60 pupils go, the coach works out at £8 each, so the total for each pupil is £17.50. If only 40 pupils go, the coach works out at £12 each, so the price rises to £21.50. The teacher explains that the coach is a fixed cost and the entry is a cost per person — which is why the price per pupil changes when the number changes.
The school decides to charge £20 and to use anything left over for a second trip later in the year.
Written for Good Learning Co.
Reading questions
- Work out the total cost of the trip if 50 pupils go.
- Show why the price per pupil falls when more pupils go, using numbers.
- At £20 each, how many pupils must go before the trip makes money? Show your working.
Working out
Working outDo the practice questions on paper, showing every step — not just the answer. Mark them yourself and circle anything you got wrong.
10–15 questions
Worked example, explained
WritingCopy one question out and write underneath, in words, why each step works.
1 question, 4–5 sentences
Problem in words
Working outWrite your own real-life problem that uses today's method, then solve it.
1 problem + solution
Saved as you type.
Part 1 of 14 · Watch & discover
How this is going
- Not looked at yet
Apply the properties of angles at a point, on a straight line, vertically opposite angles, and angles in parallel lines