Question

the right hexagonal prism shown to the right has regular hexagons as bases.
a. name all the pairs of parallel lateral faces. (faces are parallel if the planes containing the faces are parallel.)
b. what is the measure of the dihedral angle between two adjacent lateral faces? why?
quadrilaterals eaae and edde
quadrilaterals cbbc and dccd
quadrilaterals ubbu and uccu
quadrilaterals edde and feef
b. choose the correct answer below and fill in the answer box to complete your choice (type a whole number)
a. the measure of the angle is ° because this is the measure of the total degrees of the hexagonal base divided by the number of faces 8
b. the measure of the angle is ° because this is the measure of an interior angle of a hexagon, which is where the two planes representing the lateral faces intersect
c. the measure of the angle is ° because this is the measure for all dihedral angles
d. the measure of the angle is ° because two adjacent lateral faces form perpendicular planes and this is the measure of perpendicular planes

Explanation:

Step1: Identify parallel lateral - faces

In a right hexagonal prism, the pairs of parallel lateral faces are: quadrilaterals $AA'B'B$ and $DD'E'E$, quadrilaterals $BB'C'C$ and $EE'F'F$, quadrilaterals $CC'D'D$ and $FF'A'A$.

Step2: Determine dihedral - angle between adjacent lateral faces

The lateral faces of a right hexagonal prism are rectangles. The dihedral angle between two adjacent lateral faces is $90^{\circ}$ because two adjacent lateral faces form perpendicular planes.

Answer:

a. Pairs of parallel lateral faces: quadrilaterals $AA'B'B$ and $DD'E'E$, quadrilaterals $BB'C'C$ and $EE'F'F$, quadrilaterals $CC'D'D$ and $FF'A'A$.
b. D. The measure of the angle is $90^{\circ}$ because two adjacent lateral faces form perpendicular planes and this is the measure of perpendicular planes.