We are given a triangle with one exterior angle of $249^\circ$. Two of the interior angles of the triangle are $33^\circ$ and $25^\circ$. We need to find the size of the third interior angle, denoted as $a$.

1. Problem Description

We are given a triangle with one exterior angle of $249^\circ$. Two of the interior angles of the triangle are $33^\circ$ and $25^\circ$. We need to find the size of the third interior angle, denoted as $a$.

2. Solution Steps

First, we need to find the interior angle adjacent to the given exterior angle of $249^\circ$. Let's call this interior angle $b$. We know that the sum of an interior angle and its adjacent exterior angle is $180^\circ$. Therefore,

$b + 249^\circ = 360^\circ$

$b = 360^\circ - 249^\circ = 111^\circ$

(since the exterior angle is greater than $180^\circ$, it must be reflex and the adjacent interior and exterior angles must sum to $360^\circ$)

Now we have the three interior angles of the triangle: $33^\circ$, $25^\circ$, and $a$. The sum of the interior angles of a triangle is $180^\circ$. Therefore,

$a + 33^\circ + 25^\circ = 180^\circ$

$a + 58^\circ = 180^\circ$

$a = 180^\circ - 58^\circ$

$a = 122^\circ$

3. Final Answer

The size of angle $a$ is $122^\circ$.