(i) If all the angles of a hexagon are equal, find the measure of each angle.

(ii) If all the angles of a 14-sided figure are equal, find the measure of each angle.

(i) According to the properties of a polygon, if a polygon has n sides, then the sum of its interior angles is (2n - 4) x 90°.

A hexagon has 6 sides.

So, the sum of its interior angles is:

(2 x 6 - 4) x 90°

= (12 - 4) x 90°

= 8 x 90°

= 720°

Since it is given that all angles are equal, let each angle be a.

⇒ 6a = 720°

⇒ a = $\dfrac{720°}{6}$

⇒ a = 120°

Hence, the measure of each angle is 120°.

(ii) According to the properties of a polygon, if a polygon has n sides, then the sum of its interior angles is (2n - 4) x 90°.

A polygon with 14 sides is given.

So, the sum of its interior angles is:

(2 x 14 - 4) x 90°

= (28 - 4) x 90°

= 24 x 90°

= 2160°

Since it is given that all angles are equal, let each angle be a.

14a = 2160°

⇒ a = $\dfrac{2160°}{14}$

⇒ a = $\dfrac{1080°}{7}$

⇒ a = $154\dfrac{2°}{7}$

Hence, the measure of each angle is $154\dfrac{2°}{7}$.