Stage 9 - Q1 - 2 marks
Find one exterior turning angle of a regular 20-gon.
Hint
Use one exterior angle at each vertex in the same turning direction.
Stage 9 - Q2 - 2 marks
Find the side count of the regular polygon.
Hint
The side count equals the number of equal turns.
Stage 9 - Q3 - 3 marks
For a regular polygon, find the exterior angle and side count.
Hint
Use 180 degrees first, then 360 degrees.
Stage 9 - Q4 - 3 marks
One consistent exterior turn is taken at each pentagon vertex. Find the exterior turn at E.
Hint
The exterior total does not depend on the side count.
Stage 9 - Q5 - 4 marks
Can a regular polygon have an exterior angle of \(17^\circ\)? Explain.
Hint
A regular polygon needs a whole number of equal turns.
Stage 9 - Q6 - 4 marks
Can a regular polygon have an exterior angle of \(22^\circ\)? Explain.
Hint
A regular polygon needs a whole number of equal turns.
Stage 9 - Q7 - 5 marks
Compare a regular 10-gon with a regular 20-gon. Find both exterior angles and explain their ratio.
Hint
The total turn stays fixed while the number of turns doubles.
Stage 9 - Q8 - 5 marks
A regular polygon has interior angle 4 times its exterior angle. Find both angles and its number of sides.
Hint
Use the ratio in the 180-degree relationship before using a full turn.
Stage 9 - Q9 - 5 marks
One regular polygon has twice as many sides as another. Their exterior angles differ by \(\frac{45}{2}^\circ\). Find both side counts.
Hint
Write both exterior angles in terms of the smaller side count.
Stage 9 - Q10 - 3 marks
The interior angles of two regular polygons add to \(300^\circ\). Find every unordered pair of side counts \((n,m)\), with \(n\le m\).
Hint
Use positive factor pairs of 36 after subtracting 6 from each side count.