The problem states that an arrowhead and a parallelogram are joined. An equilateral triangle is formed using one of the parallelogram's diagonals. We need to find the size of angle a.

Step 1: Analyze the given information and diagrams.
The problem states that an arrowhead and a parallelogram are joined. An equilateral triangle is formed using one of the parallelogram's diagonals. We need to find the size of angle $a$.

From the diagrams:

• The arrowhead has two sides marked with a single dash. Let the length of these sides be $s$.
• The parallelogram is joined to the arrowhead along one of its sides, which is also marked with a single dash. So, this side of the parallelogram has length $s$.
• In the combined figure, a diagonal of the parallelogram is drawn (dashed line). This diagonal is also marked with a single dash, meaning its length is $s$.
• This diagonal, along with two sides