A student draws two different regular polygons - OCR - GCSE Maths - Question 11 - 2023 - Paper 5

The difference between the angles is given as: $p - q = 32^\circ$

We can solve these two equations simultaneously.

From the second equation: $p = q + 32^\circ$

Substituting this into the first equation: $(q + 32^\circ) + q = 112^\circ$

This simplifies to: $2q + 32^\circ = 112^\circ$

Subtracting $32^\circ$ from both sides: $2q = 80^\circ$

Dividing by 2: $q = 40^\circ$

Substituting $q$ back to find $p$: $p = 40^\circ + 32^\circ = 72^\circ$

To find the number of sides of each polygon, we use the formula for the exterior angle: $ext{Number of sides} = \frac{360^\circ}{\text{exterior angle}}$

For $p$: $\text{Number of sides} = \frac{360^\circ}{72^\circ} = 5$

For $q$: $\text{Number of sides} = \frac{360^\circ}{40^\circ} = 9$

Thus, the first polygon has 5 sides (pentagon) and the second polygon has 9 sides (nonagon).