The problem asks to find the size of the angle $m$ in the given diagram. We know that angles around a point sum to $360^\circ$. However, since the diagram shows only half of the angles around the point, and we have straight lines going through the point, the sum of the angles shown must be half of $360^\circ$, which is $180^\circ$.

1. Problem Description

The problem asks to find the size of the angle $m$ in the given diagram. We know that angles around a point sum to $360^\circ$. However, since the diagram shows only half of the angles around the point, and we have straight lines going through the point, the sum of the angles shown must be half of $360^\circ$, which is $180^\circ$.

2. Solution Steps

The sum of the angles in a straight line is $180^\circ$. Therefore, the sum of the angles shown in the figure should be $180^\circ$. We have the angles $13^\circ$, $24^\circ$, $15^\circ$, and $m$.

Thus, we have

$13 + 24 + 15 + m = 180$

$52 + m = 180$

$m = 180 - 52$

$m = 128$

3. Final Answer

The size of angle $m$ is $128^\circ$.