How many ways are there to move from one corner of a cube to the diagonally opposite corner, in three moves, each of which travels along one edge of the cube

6 ways

there are 6 ways to move from one corner of a cube to the diagonally opposite corner in three moves

Step-by-step explanation:

Given that;

-It's restricted to three moves.

-It has to move from one diagonal to its opposite diagonal.

-it can only move through the edges.

Hence, in the first move.

We have three(3) different options that is three different possible moves that can lead us to the final destination.

The second move.

We have two (2) different possible moves each

The last move

We have just one(1) possible move.

To get the total possible ways, we will multiply the possible options for each move.

Move 1 = 3 options

Move 2 = 2 options each

Move 3 = 1 option each

3 × 2 × 1 = 6 ways

answer: (c) m∠qpo + (2x + 16)° = 180°

step-by-step explanation:

the opposite angles of a quadrilateral are supplementary.

so, ∠o + ∠q = 180°   and   ∠p + ∠r = 180°

since ∠r = 2x + 16°, we can use substitution as follows:

∠p + ∠r = 180°

∠p + (2x + 16)° = 180°