Triangles, interior and exterior polygon angles

(a) $36^\circ$

• M1 Dividing $360$ by $10$.
• A1 Correct answer: $36^\circ$.

(b) $144^\circ$

• B1 Correct answer: $144^\circ$.

(a) $9$

• M1 Find the supplementary exterior angle.
• M1 Divide a full turn by the exterior angle.
• A1 Correct answer: $9$

(b) A polygon has a whole number of edges; a non-integer result would mean the proposed regular polygon cannot exist.

• C1 Correct conclusion with supporting reasoning: A polygon has a whole number of edges; a non-integer result would mean the proposed regular polygon cannot exist.

(a) 15

• P1 Finding the exterior angle, $24^\circ$.
• P1 Dividing $360$ by their exterior angle.
• A1 Correct answer: 15 sides.

(b) $2340^\circ$

• M1 $(n - 2) \times 180$ with their $n$, or $n \times 156$.
• A1 Correct answer: $2340^\circ$.