The problem asks us to find the size of angle $f$. We are given that the angle vertically opposite to the angle $84^{\circ}$ is split into two angles, $f$ and $21^{\circ}$.

1. Problem Description

The problem asks us to find the size of angle $f$. We are given that the angle vertically opposite to the angle $84^{\circ}$ is split into two angles, $f$ and $21^{\circ}$.

2. Solution Steps

Vertically opposite angles are equal. Therefore, the angle opposite to $84^{\circ}$ is also $84^{\circ}$.

The angle $84^{\circ}$ is composed of angle $f$ and the angle $21^{\circ}$.

So, we can write the equation $f + 21^{\circ} = 84^{\circ}$.

To find the value of $f$, subtract $21^{\circ}$ from both sides of the equation.

$f = 84^{\circ} - 21^{\circ}$

$f = 63^{\circ}$

3. Final Answer

The size of angle $f$ is $63^{\circ}$.