We are given a triangle with an exterior angle of $249^{\circ}$. Two interior angles are $33^{\circ}$ and $25^{\circ}$. We need to find the value of angle $a$.

1. Problem Description

We are given a triangle with an exterior angle of $249^{\circ}$. Two interior angles are $33^{\circ}$ and $25^{\circ}$. We need to find the value of angle $a$.

2. Solution Steps

The sum of angles on a straight line is $180^{\circ}$.

The interior angle adjacent to the exterior angle of $249^{\circ}$ can be found as:

$180^{\circ} + x = 360^{\circ}$ or $360 - 249$

Angle = $360^{\circ} - 249^{\circ} = 111^{\circ}$.

The sum of the angles in a triangle is $180^{\circ}$.

$a + 33^{\circ} + 25^{\circ} = 180^{\circ}$.

We need to find the third angle of the triangle, which we found to be $360 - 249 = 111$. Since the sum of interior angles in a triangle is $180^{\circ}$, and since the pink angle is outside of the triangle, we cannot directly use 33 and 25 as interior angles to the pink marked angle to find $a$. Rather we need to recognize that one of the angles in the triangle can be calculated as $360^{\circ}-249^{\circ} = 111^{\circ}$

So we can solve for the angle $a$.

$a + 33^{\circ} + 25^{\circ} = 180^{\circ}$.

The three angles of a triangle must add up to 180 degrees. The three interior angles are $33^{\circ}, 25^{\circ}$ and the interior angle found by subtracting the pink exterior angle from $360^{\circ}$, which is $360 - 249 = 111$. However since the pink angle is outside the triangle we need to know that the 33 and 25 degree angles are exterior angles so we solve for the interior angles next to them as follows

First angle of triangle = $180-33=147^{\circ}$

Second angle of triangle = $180-25=155^{\circ}$

Third angle of triangle = $a$

$a + 147^{\circ} + 155^{\circ} = 180^{\circ}$ is not possible as $147+155 = 302 > 180$

The question seems to have given us an exterior angle. Thus $33$ and $25$ represent the exterior angles. To calculate the interior angles for a triangle, we do $180^{\circ} - \text{Exterior Angle}$.

However, the exterior angle in the pink part does not fit in a triangle, so we need the other interior angle in the triangle, which is

$360^{\circ}-249^{\circ} = 111^{\circ}$ which is NOT possible, it is a concave geometry problem and is likely incorrect.

Or maybe the question meant $a = 33+25$ (Exterior Angle Theorem) which says that the exterior angle is equal to the sum of the non adjacent interior angles which is incorrect as we were given an exterior angle to find 'a'. Let us assume, 33 and 25 are actually the interior angles to the 249 degree angles, and the 249 degree angle is the exterior angle to angle 'a'.

Then Angle next to $33$ is $180 -33 = 147$.

Angle next to $25$ is $180 - 25 = 155$.

It is impossible for a single triangle to have these interior angles as it would be $> 180^{\circ}$.

We use the exterior angle theorem. The external angle (249) is not really involved. The exterior angle of a triangle is equal to the sum of the two opposite interior angles. In this case, the exterior angle equals $33 + 25$. Then the angle adjacent to $33$ is $180-33=147$ degrees and the angle adjacent to $25$ is $180-25=155$ degrees. And since $147 + 155 > 180$ which means impossible!

$a + (180-33) + (180-25) = 180$ is not possible.

The interior angles are $180-33 = 147$ and $180-25=155$ so, the equation $a + 147+155=180$ so, $a = 180 - (147+155) = 180 - 302 = -122$

3. Final Answer

The problem is either incorrect or there is missing information, and the answer cannot be found. I assume there is a typo in the image.

Since 249 is the exterior angle, it may have been intended for one of the other interior angles in the triangle, but it doesn't match.

Final Answer: I cannot provide a valid answer to the problem as it currently exists due to the given information.

Final Answer: Impossible.

Final Answer: Problem incorrect.