Mathematics

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50 mins

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+65 XP

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Chromebook/Laptop/PC or iPad/Tablet
IWB/Projector/Large Screen

Angles in Triangles: Sum Is 180°

Discover that the three interior angles of any triangle always sum to 180°. Learn to find missing angles and recognise equilateral, isosceles and right-angled triangles by their angle properties.

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1 Getting Started
2 Watch the Pattern: Three Angles, One Total
3 Try Together at the IWB
4 Sketch and Calculate in Your Jotter
5 Your Turn: Six Triangle Problems
Pupil practice
Going further
Homework

1 - Getting Started

Three players line up on the pitch to make a passing triangle. Picture any code you play: Gaelic football, rugby, hockey, soccer. Player A stands at one corner, Player B at the second, Player C at the third. The angle at Player A's corner is 50° and the angle at Player B's corner is 70°. What angle do they make at Player C's corner: 30°, 50°, or 60°? Share your hunch and say what helped you guess.

Today we discover a property that holds for every triangle: no matter how big, how small, how stretched or how squished, the three interior angles always add up to exactly the same total. By the end of the lesson you will be able to find any missing angle in a triangle in one short calculation.

Teacher Notes

Spend 3–4 minutes on the hook. Name a mix of sports as you set the scene so the framing lands for the full classroom (Gaelic, rugby, hockey, soccer all work for the passing-triangle image). Take three or four hunches without confirming the answer. If a pupil already calls out '180°', revoice it but don't dwell — that's the headline reveal for the model step. Keep predictions visible on a side panel so you can return to them after the model.

👇 Mark your steps as done as you complete them.

+5 XP

2 - Watch the Pattern: Three Angles, One Total

Watch four triangles on the board — scalene, equilateral, isosceles, right-angled. Each one has different angles, but every time you add the three together you get the same answer: 180°. All three angles are labelled on every triangle so you can read off each one and confirm the running sum yourself.

The rule: angle A + angle B + angle C = 180°. If you ever need to find a missing angle, subtract the two you know from 180°.

Teacher Notes

Walk each snapshot aloud. For the scalene, cover the 60° with your hand and ask 'if you only saw 50° and 70°, how would you work the third out?' — narrate 50 + 70 = 120, so 180 − 120 = 60. For the equilateral, ask 'what's special?' (all sides equal, every angle 60°). For the isosceles, get pupils to notice the two matching base angles. For the right-angled, emphasise that the two non-right angles MUST sum to 90°. Do not move on until the class can recite 'every triangle sums to 180°' in unison.

👇 Mark your steps as done as you complete them.

+10 XP

3 - Try Together at the IWB

Now we explore together at the IWB. The teacher calls out a triangle to make and an individual pupil drags a vertex to morph the triangle into that shape. As they drag, all three interior angles recompute live — and the sum readout always holds at 180° no matter what shape we land on.

Triangles to try:

tall and skinny — what happens to the smallest angle?
almost right-angled — drag a corner near 90°
very obtuse — one angle bigger than 90°, the other two share what's left
as close to equilateral as you can — all three near 60°

Predict roughly where each angle will land before the drag finishes, then read the actual measurements off the readout.

Drag the corners — the sum stays at 180°

Teacher Notes

Call up individual pupils to drag a vertex into each shape the class calls out. The sum readout always holds at exactly 180° — the widget computes the angles from the live vertex positions, so no nudging is needed. Use that as the headline: 'no matter what shape we make, the three angles share 180° between them.' Pause after each drag and ask the class to read off the three angle values, then confirm the sum aloud.

+15 XP

4 - Sketch and Calculate in Your Jotter

COPYBOOK MOMENT

In your jotter, draw each triangle as the IWB shows it, label the two known angles, then write the calculation for the third angle underneath. Use this layout — one triangle then one calculation, neatly stacked:

180° − (40° + 80°) = 60°
180° − (25° + 90°) = 65°
180° − (50° + 50°) = 80°
180° − (20° + 110°) = 50°

Keep your triangles small but neat — the calculation matters more than the drawing.

Teacher Notes

Walk the rows glancing at the calculation format: '180° minus, brackets, sum, equals'. No individual marking — this is parallel-work accountability, not assessment. Look for pupils who are computing the sum first then subtracting, versus pupils who subtract one angle then the other; both are fine, name the choice aloud for the class.

+10 XP

5 - Your Turn: Six Triangle Problems

Six triangles on the board. For each, two angles are given. Find the third, then name the type (equilateral, isosceles, right-angled, or scalene).

Quick reminder: scalene means all three angles different; obtuse means one angle bigger than 90°.

Stretch yourself on the last one: a triangle has angles in the ratio 1 : 2 : 3. Two of the angles work out as 30° and 60°. Can you find the third and name the type?

Find the missing angle in each triangle

Teacher Notes

Individual pupils come up to the IWB to solve each challenge in turn; the rest of the class works mentally in their jotters and predicts. After each, ask 'what TYPE of triangle is this?' — weave in equilateral / isosceles / right-angled / scalene vocabulary as you go. Reinforce the quick reminders pupils see on screen: scalene = all three angles different; obtuse = one angle bigger than 90°. For the ratio stretch (1 : 2 : 3), walk the parts-of-a-whole reasoning aloud: 'There are 1 + 2 + 3 = 6 parts altogether. The whole is 180°, so 1 part = 180° ÷ 6 = 30°. That means the three angles are 1 × 30° = 30°, 2 × 30° = 60° and 3 × 30° = 90°.' The IWB shows 30° and 60° already in place so pupils can confirm the third is 90° — a genuinely surprising right-angled triangle hides inside that ratio.

+15 XP

Pupil practice

Module 7 · Shape and Space: 2D and 3D Shape, Symmetry, Angles, Coordinates and Compass Shape & Space

Activity Book — Page 88

Lesson 88 · Angles in Triangles: Sum Is 180°

Download Activity Book page (PDF)

Going further

Extension challenges

If you finish early — try these harder challenges on your device.

Polygon angles

Practice at home

Homework

Device required

Tonight's homework — work through these on your device.

Polygon angles

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This lesson is copyright of Coding Ireland 2017 - 2025. Unauthorised use, copying or distribution is not allowed.

Angles in Triangles: Sum Is 180°

Teacher Class Feed

1 - Getting Started

2 - Watch the Pattern: Three Angles, One Total

3 - Try Together at the IWB

Drag the corners — the sum stays at 180°

4 - Sketch and Calculate in Your Jotter

5 - Your Turn: Six Triangle Problems

Find the missing angle in each triangle

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