Mathematics • Year 7 • Unit 3 • Lesson 18
Geometric Reasoning — Real World
Apply multi-step angle reasoning to roof trusses, ramps, sports markings, regular tiles and street layouts. Every line in your working needs the right named reason.
1. Word problems
Each problem needs a chain of 2 or 3 angle facts. Show your working — and remember: every line gets a written reason in brackets.
1.1 — Roof truss. A symmetric (isosceles) triangular roof truss has its apex at the top. The angle at the apex is 80°.
(a) State the size of each base angle, with reason.
(b) If the truss is sitting on a horizontal beam, what is the angle between one sloped side and the horizontal beam? 3 marks
1.2 — Street layout. Bond Street and Carter Street run parallel east–west across a town. Davis Avenue is a transversal that crosses Bond Street at 70° (measured above and right of the crossing).
(a) Find the angle Davis Avenue makes with Carter Street at the corresponding crossing — give the named reason.
(b) Find the co-interior angle on the SAME side of Davis Avenue at Carter Street — give the named reason. 2 marks
1.3 — Soccer corner kick. The corner of a soccer pitch is exactly 90°. A line painted from the corner to a player makes an angle of 35° with the goal line. Find the angle the line makes with the sideline.
2 marks
1.4 — Regular octagon tile. A stop-sign-shaped tile is a regular octagon (8 equal sides, 8 equal angles).
(a) Find the interior angle sum of an octagon.
(b) Find the size of one interior angle. 2 marks
1.5 — Ramp + wall. A wheelchair ramp meets a vertical wall. The ramp makes an angle of 12° with the horizontal ground. Find the angle between the ramp and the wall, with reasons.
3 marks
2. Explain your thinking
This question is about communication, not just answers. Use full sentences. 4 marks
2.1 A classmate solves a triangle problem and writes: "x = 60. Done." The teacher gives them 0 marks even though x = 60 is the correct answer. In your own words, explain (i) WHY the teacher gave 0, (ii) what the classmate should have written, and (iii) give your own example of a fully reasoned answer using a named angle fact (it can be made-up — just show the format).
How did this worksheet feel?
What I'll revisit before next class:
1.1 — Roof truss
(a) Base angles equal (isosceles triangle). Each = (180 − 80) ÷ 2 = 50° (∠ sum of △).
(b) The truss sits on the horizontal beam, so the angle between one sloped side and the beam IS one of the base angles = 50°.
1.2 — Street layout
(a) Corresponding angle at Carter Street = 70° (corr ∠s, Bond ∥ Carter).
(b) Co-interior angle = 180 − 70 = 110° (co-int ∠s, Bond ∥ Carter).
1.3 — Soccer corner
Sideline angle = 90 − 35 = 55° (angles on a perpendicular corner add to 90°).
1.4 — Regular octagon
(a) Sum = (8 − 2) × 180 = 6 × 180 = 1080°.
(b) Each angle = 1080 ÷ 8 = 135°.
1.5 — Ramp + wall
The wall, ground and ramp form a right triangle. The angle where the ground meets the wall is 90°. The ramp's angle with the ground is 12°. So the third angle of the triangle (between ramp and wall) = 180 − 90 − 12 = 78° (∠ sum of △).
2.1 — Explain your thinking (sample response)
The teacher gave 0 marks because in geometric reasoning, the marker is testing whether you can justify your answer — not just guess or compute it. Writing "x = 60. Done." gives a number but no evidence that you used a known angle fact. The marker can't tell whether you reasoned, copied, or guessed. The classmate should have written something like: "x = 180 − 60 − 60 = 60° (∠ sum of △)" — value, calculation, and a named reason in brackets. For example, in my own working: "∠ABC = 180 − 75 = 105° (co-int ∠s, AB ∥ CD)" shows the value, the calculation 180 − 75, and the named reason "co-interior angles on parallel lines add to 180°". Every step in geometric reasoning needs this format: value = calculation (reason).
Marking: 1 mark for explaining why no reason loses marks; 1 mark for correctly writing the format value = calc (reason); 1 mark for a clear made-up example; 1 mark for full-sentence communication.