The problem asks us to find the size of angle $a$ in a quadrilateral. The other three angles in the quadrilateral are given as $121^\circ$, $105^\circ$, and $82^\circ$.

1. Problem Description

The problem asks us to find the size of angle $a$ in a quadrilateral. The other three angles in the quadrilateral are given as $121^\circ$, $105^\circ$, and $82^\circ$.

2. Solution Steps

The sum of the interior angles in a quadrilateral is $360^\circ$. Therefore, we can write the equation:

$a + 121^\circ + 105^\circ + 82^\circ = 360^\circ$

$a + 308^\circ = 360^\circ$

Subtract $308^\circ$ from both sides:

$a = 360^\circ - 308^\circ$

$a = 52^\circ$

3. Final Answer

The size of angle $a$ is $52^\circ$.