Florence’s Maths
Lesson five
The week,
all together
A gentler last lesson, Florence — no new rules, just a chance to use everything.

The end of the week

This is the fifth and last lesson of the week, Florence — and it is a gentler one. There is nothing new to learn here. Everything in it, you have already met.

Lesson 5 is a chance to use the week's ideas all together, mixed up, the way real questions come — you have to spot which rule fits before you can use it. A couple of them lean on more than one rule at once.

Take them slowly. There is no timer, and the working is always one tap away under ‘show me how’. Tap Continue when you're ready.

The week in one place

Here is the whole week, gathered in one place. Nothing below is new — you have met every line of it.

  • Angles on a straight line add up to 180°.
  • Angles around a point add up to 360°.
  • Where two lines cross, vertically opposite angles are equal.
  • Across parallel lines: corresponding angles and alternate angles are equal; co-interior angles add up to 180°.
  • The angles in a triangle add up to 180° — and an isosceles triangle has two equal angles.
  • The angles in a quadrilateral add up to 360°; in any polygon, they total (n − 2) × 180°.
  • The exterior angles of any polygon add up to 360°.

No question here

Just have a play

Before the questions, here is the triangle from Lesson 3 again. Drag its corners and watch the three angles move — and notice that however you pull it about, the total stays at 180°.

Nothing is marked or recorded on this screen. It is only here to wake the idea up before you begin.

Try it yourself
Drag any corner. The three angles always add up to 180°.
A B C
A 66° B 53° C 61° Total 180°

Question 1

A straight line, to start.

Two angles sit together on a straight line. One of them is 124°. What is the other?

Angles on a straight line add up to 180°.

So the other is 180° − 124° = 56°.

Question 2

Three angles meet at a point and fill the space all the way around it. Two of them are 140° and 95°. What is the third?
°
Type the number of degrees, then tap Check.

Angles around a point add up to 360°.

140° + 95° = 235°.

Then 360° − 235° = 125°.

Question 3

Two straight lines cross. One of the four angles they make is 47°. What is the angle vertically opposite it?

When two lines cross, the angles opposite each other are equal.

So the vertically opposite angle is 47°.

Question 4

Now the parallel-line pairs from Lesson 2.

A straight line crosses two parallel lines. One angle is 68°. What is the corresponding angle, in the matching position at the other crossing?

Corresponding angles — in matching positions at each crossing — are equal.

So it is 68°.

Question 5

Two co-interior angles lie between a pair of parallel lines, on the same side of the transversal. One of them is 124°. What is the other?
°
Type the number of degrees, then tap Check.

Co-interior angles add up to 180°.

So the other is 180° − 124° = 56°.

Question 6

On to triangles.

A triangle has angles of 43° and 67°. What is its third angle?

The three angles of a triangle add up to 180°.

43° + 67° = 110°.

Then 180° − 110° = 70°.

Question 7

An isosceles triangle has an apex angle of 50°. Its two base angles are equal to each other. What is the size of one base angle?
°
Type the number of degrees, then tap Check.

The three angles add up to 180°.

Take away the apex: 180° − 50° = 130°.

The two equal base angles share it: 130° ÷ 2 = 65°.

Question 8

And the four-sided shapes.

A quadrilateral has three angles of 100°, 80° and 95°. What is the fourth angle?

The four angles of a quadrilateral add up to 360°.

100° + 80° + 95° = 275°.

Then 360° − 275° = 85°.

Question 9

The angles of an n-sided polygon add up to (n − 2) × 180°. What do the six angles of a hexagon add up to?

Use (n − 2) × 180° with n = 6.

(6 − 2) × 180° = 4 × 180° = 720°.

Question 10

The last one — and it uses both ends of the week at once.

A regular hexagon has six equal sides. Its exterior angles add up to 360°, so each exterior angle is 60°. At each corner, the interior angle sits on a straight line with the exterior angle. What is each interior angle of the regular hexagon?

Each exterior angle is 360° ÷ 6 = 60°.

The interior angle is on a straight line with the exterior angle.

So the interior angle is 180° − 60° = 120°.

An angle hunt

One last thing, Florence — and there is nothing to tap or type for this one. It is an invitation, not a task.

Now that you know what to look for, angles are everywhere. Some time today, see how many of the week's ideas you can spot away from the screen:

  • The corner of a table, a book or a doorway — right angles, 90°.
  • A pair of scissors held open, or an open laptop — two lines crossing, with vertically opposite angles.
  • Floor tiles, a window frame, the panels on a football — polygons fitting together.
  • A ladder leaning on a wall, or the hands of a clock — angles on a line, angles around a point.

If the weather is kind, take the hunt outside — fences, rooftops, road signs. There is nothing to write down. It is just a way of noticing that the maths you did this week is describing the actual world around you.

Before you finish

That's Lesson 5 — and the whole of Week 1 — finished, Florence.

Five lessons. You started with a single straight line, and you have ended with the angles of any polygon there is. You did every step of it on your own, at your own pace. That is exactly how this is meant to work.

When you next talk maths with me or your mum, it might be worth saying how the week felt — which lessons clicked, which you'd like another look at. The questions you flagged will help with that.

Take a proper break now. Week 2 will be waiting whenever you're ready — and it moves to something new: drawing with a compass and a straight edge. Well done.

Week one complete

You can close this page now — or step back through any question you'd like to try again.