The correct answer is Option A: 20.
       To find the number of diagonals in a polygon, we can use the formula:
     \[ \text{Number of diagonals} = \frac{n(n-3)}{2} \]
     where \( n \) is the number of sides (or vertices) of the polygon.
     For an octagon, \( n = 8 \).
     Step-by-step Calculation:
     ● Step 1: Substitute \( n = 8 \) into the formula:  
       \[ \text{Number of diagonals} = \frac{8(8-3)}{2} \]
     ● Step 2: Simplify the expression inside the parentheses:  
       \[ 8 - 3 = 5 \]
     ● Step 3: Multiply the results:  
       \[ 8 \times 5 = 40 \]
     ● Step 4: Divide by 2 to find the number of diagonals:  
       \[ \frac{40}{2} = 20 \]
     Therefore, the number of diagonals that can be drawn by joining the vertices of an octagon is 20.