Hint
Use the stated units and precision. Divide 360° by the number of equal exterior turns.
Worked solution
(a)
Divide 360° by the number of equal exterior turns.
One full turn shared equally gives \(72\)°.
Answer: \(72\)
(b)
Use the straight-line supplement of an exterior angle.
Subtract the exterior angle \(72\)° from 180°, giving \(108\)°.
Answer: \(108\)
(c)
Multiply n−2 by the triangle angle sum.
There are 3 triangles in a decomposition, giving 540°.
Answer: \(540\)
Maths4U indicative marking guidance
Maths4U indicative marking guidance, not an official mark scheme. Credit complete valid alternative methods and consequential reasoning. An unexplained result does not earn a method mark.
(a) · 2 marks
- 1 mark: Divide 360° by the number of equal exterior turns.
- 1 mark: Give the correct requested result, retaining signs, units and any domain restrictions.
Alternative methods: Any complete mathematically valid alternative method with the same restrictions and equivalent exact result is acceptable.
Common error: Keep intermediate values exact until the final step.
(b) · 2 marks
- 1 mark: Use the straight-line supplement of an exterior angle.
- 1 mark: Give the correct requested result, retaining signs, units and any domain restrictions.
Alternative methods: Any complete mathematically valid alternative method with the same restrictions and equivalent exact result is acceptable.
Common error: Check the answer against the original conditions.
(c) · 2 marks
- 1 mark: Multiply n−2 by the triangle angle sum.
- 1 mark: Give the correct requested result, retaining signs, units and any domain restrictions.
Alternative methods: Any complete mathematically valid alternative method with the same restrictions and equivalent exact result is acceptable.
Common error: Keep intermediate values exact until the final step.
Total: 6 marks.