Question 1 The size of each exterior angle of a regular polygon is $$ 360^{\circ} $$. What is the sum of the interior angles? (3 marks)

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Let $$ n $$ be the number of sides of the polygon. For any regular polygon, the measure of each exterior angle is given by

$$
\frac{360^\circ}{n}.
$$

According to the problem, each exterior angle is $$ 360^\circ $$. Therefore, we set

$$
\frac{360^\circ}{n} = 360^\circ.
$$

Multiplying both sides by $$ n $$ gives

$$
360^\circ = 360^\circ \, n,
$$

and dividing both sides by $$ 360^\circ $$ we obtain

$$
n = 1.
$$

However, a polygon must have at least 3 sides. Since $$ n = 1 $$ does not satisfy the definition of a polygon, no regular polygon exists with an exterior angle of $$ 360^\circ $$. Consequently, the sum of the interior angles is undefined under the given condition.
There is no regular polygon with an exterior angle of $$ 360^\circ $$, so the sum of the interior angles is undefined.

Question 1 The size of each exterior angle of a regular polygon is \( 360^{\circ} \). What is the sum of the interior angles? (3 marks)

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