The problem asks us to find the size of angle $a$ in a quadrilateral, given the measures of the other three angles: $112^{\circ}$, $103^{\circ}$, and $84^{\circ}$.

1. Problem Description

The problem asks us to find the size of angle $a$ in a quadrilateral, given the measures of the other three angles: $112^{\circ}$, $103^{\circ}$, and $84^{\circ}$.

2. Solution Steps

The sum of the interior angles of a quadrilateral is $360^{\circ}$.

Therefore, we have the equation:

$a + 112^{\circ} + 103^{\circ} + 84^{\circ} = 360^{\circ}$

Combining the known angles, we get:

$a + 299^{\circ} = 360^{\circ}$

Subtracting $299^{\circ}$ from both sides, we find the value of $a$:

$a = 360^{\circ} - 299^{\circ}$

$a = 61^{\circ}$

3. Final Answer

The size of angle $a$ is $61^{\circ}$.