How many diagonals can be drawn from a vertex of an octagon?
6
7
5
8

For each vertex of an octagon, we can draw a line to each of the 7 other vertices. Out of the 7, 2 are to adjacent vertices, so they are not diagonals.

That leaves us with 5 diagonal for each of the vertices, giving a total of 5*8=40 diagonals.

However, diagonals are not considered directional, i.e. drawing from each end is the same diagonal, so we need to reduce the number of diagonal by half. The total number of diagonals is therefore 40/2=20.

In the attached diagram, we see the five diagonals drawn from vertex a.

3< x< 5

step-by-step explanation:

|x - 4| < 1

there are two solutions, one positive and one negative.   remember to flip the inequality when taking the negative solution

x-4 < 1       x-4 > -1

add 4 to each side

x-4+4 < 1+4       x-4+4 > -1+4

x< 5                 x> 3

3< x< 5