Mathematics 7–10 · Year 7
Angle sum of a triangle: torn corners on a straight line, checked with a protractor
Measurement and space
The idea
The three interior angles of any triangle, placed together, make a straight angle, so they sum to 180 degrees whatever the triangle's shape.
What you need
- 3 paper triangles per learner of different types (acute, obtuse, right-angled), cut from A4 paper
- Protractor (180 degree, 10 cm)
- Ruler and pencil
How to do it
- Measure the three angles of each triangle with the protractor to the nearest degree and add them; record the sum for each triangle.
- Mark each corner with a different colour, tear the three corners off one triangle and place them with their vertices together against a ruled straight line.
- Repeat the tearing for the obtuse and right-angled triangles.
- Draw a line through one vertex parallel to the opposite side and mark the alternate angles to explain why the corners fill the straight angle.
- Extension: cut a quadrilateral into two triangles along a diagonal and predict its angle sum before measuring.
What you should see
Each measured sum lies between 177 and 183 degrees, since each protractor reading carries about ±1 degree and three readings are added; sums outside that band point to a misread scale (reading 120 for 60 is the common one). The three torn corners fit the straight line with no gap and no overlap for all three triangle types. The quadrilateral gives two triangles and a measured sum near 360 degrees. The learner knows it worked when the obtuse and acute triangles give the same 180 within reading error.
What changes
This activity lists no variables to change, measure and keep the same.
Common misconceptions
Each of these ideas is wrong, and the activity is a chance to test it.
- A bigger triangle has a bigger angle sum.
- An obtuse triangle has an angle sum over 180 degrees.
- Angle size depends on the length of the arms drawn.
Safety card
Hazards
No hazard is listed.
Controls
No control is listed.
Note
No chemicals or heat are used, so the NSW Department of Education Chemical Safety in Schools package does not apply; ordinary classroom supervision.
Curriculum references
The NSW syllabus outcomes and Australian Curriculum v9 codes this activity supports. They are references, not a verified or complete curriculum alignment.
- Mathematics K–10 Syllabus (2022), Stage 4 Properties of geometrical figures; page read 2026-09-22MA4-GEO-C-01
- Australian Curriculum v9AC9M7M05
Sources
The pages the author read to write this activity.