Stage 9 - Q1 - 2 marks
Find the interior angle sum of any 5-gon.
Hint
Count triangles from one vertex.
Stage 9 - Q2 - 2 marks
A polygon has interior angle sum \(720^\circ\). Find its number of sides.
Hint
The number of triangles is two fewer than the number of sides.
Stage 9 - Q3 - 3 marks
Find angle \(E\) of the pentagon.
Hint
A pentagon contains three triangles.
Stage 9 - Q4 - 3 marks
Find angle \(F\) of the hexagon.
Hint
A hexagon has angle sum 720 degrees.
Stage 9 - Q5 - 4 marks
In the pentagon, \(A=B=90^\circ\), \(C=E=x^\circ\), and D is given. Find \(x\).
Hint
Use the repeated unknown twice in the angle sum.
Stage 9 - Q6 - 4 marks
In the pentagon, \(A=B=90^\circ\), \(C=E=x^\circ\), and D is given. Find \(x\).
Hint
Use the repeated unknown twice in the angle sum.
Stage 9 - Q7 - 5 marks
A learner says every polygon has angle sum \(360^\circ\). Use a 12-gon to test the statement.
Hint
Compare the required number of triangles.
Stage 9 - Q8 - 5 marks
A marked point inside a convex 4-gon is joined to every vertex. Use the resulting triangles to derive its interior angle sum.
Hint
The central angles are not polygon corner angles.
Stage 9 - Q9 - 5 marks
Can a polygon have an interior angle sum of \(990^\circ\)? Explain.
Hint
A number of sides must be a whole number at least 3.
Stage 9 - Q10 - 3 marks
Polygon P has three more sides than polygon \(Q\). The interior angle sum of P is twice that of Q. Find both numbers of sides and verify the sums.
Hint
P has \(n+3\) sides, so it has \(n+1\) triangles in the vertex triangulation.