The problem requires finding the size of angle $q$ in the given figure. The figure depicts a concave quadrilateral with one interior angle labelled as $235^{\circ}$, and two other interior angles of a triangle being $47^{\circ}$ and $24^{\circ}$.

1. Problem Description

The problem requires finding the size of angle $q$ in the given figure. The figure depicts a concave quadrilateral with one interior angle labelled as $235^{\circ}$, and two other interior angles of a triangle being $47^{\circ}$ and $24^{\circ}$.

2. Solution Steps

First, we need to find the interior angles of the quadrilateral where the given angles $47^{\circ}$ and $24^{\circ}$ are located.

Since the sum of angles around a point is $360^{\circ}$, we can find the interior angle adjacent to the $235^{\circ}$ angle by subtracting $235^{\circ}$ from $360^{\circ}$.

$360^{\circ} - 235^{\circ} = 125^{\circ}$.

Now, the quadrilateral has angles $47^{\circ}$, $24^{\circ}$, and $125^{\circ}$. Let the fourth angle be $q$. The sum of the interior angles in any quadrilateral is $360^{\circ}$. Therefore,

$47^{\circ} + 24^{\circ} + 125^{\circ} + q = 360^{\circ}$

$196^{\circ} + q = 360^{\circ}$

$q = 360^{\circ} - 196^{\circ}$

$q = 164^{\circ}$

3. Final Answer

The size of angle $q$ is $164^{\circ}$.