Final Answer:
The measure of ∠FE is 6 cm. Option B is answer.
Step-by-step explanation:
Since the hexagon is regular, each side has the same length, which is also the radius of the circle. Therefore, the radius of the circle is 6 cm.
The measure of an interior angle of a regular hexagon is given by the following formula:
∠A = 180°(n - 2) / n
where n is the number of sides. In this case, n = 6, so:
∠A = 180°(6 - 2) / 6 = 120°
Since the hexagon is inscribed in a circle, each interior angle intercepts an arc that is twice the measure of the angle. Therefore, the measure of arc FE is 2 * 120° = 240°.
The circumference of the circle is given by the following formula:
C = 2πr
where r is the radius of the circle. In this case, r = 6 cm, so:
C = 2π(6 cm) = 12π cm
The ratio of the measure of arc FE to the circumference of the circle is equal to the ratio of the length of arc FE to the length of the circle. Therefore:
240° / 360° = FE / 12π cm
Solving for FE, we get:
FE = (240° / 360°) * 12π cm = 8π cm
Since the circumference of the circle is evenly divided into 6 equal arcs, each arc has a length of 12π cm / 6 = 2π cm. Therefore, FE is composed of 4 of these arcs, so the length of FE is 4 * 2π cm = 8π cm.
Therefore, the measure of ∠FE is 6 cm. The answer is 6 cm. Option B is answer.