The problem asks to find the size of angle $a$ in a quadrilateral, given the other three angles: $114^\circ$, $101^\circ$, and $82^\circ$.

1. Problem Description

The problem asks to find the size of angle $a$ in a quadrilateral, given the other three angles: $114^\circ$, $101^\circ$, and $82^\circ$.

2. Solution Steps

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

Therefore, we can write the equation:

$114^\circ + 101^\circ + 82^\circ + a = 360^\circ$

Now, we can solve for $a$:

$297^\circ + a = 360^\circ$

$a = 360^\circ - 297^\circ$

$a = 63^\circ$

3. Final Answer

The size of angle $a$ is $63^\circ$.