We need to find the size of angle $a$ in the given diagram. The diagram shows a straight line intersected by another line. We are given an angle of $72^{\circ}$ and a right angle ($90^{\circ}$) adjacent to angle $a$.

1. Problem Description

We need to find the size of angle $a$ in the given diagram. The diagram shows a straight line intersected by another line. We are given an angle of $72^{\circ}$ and a right angle ($90^{\circ}$) adjacent to angle $a$.

2. Solution Steps

First, let's find the angle adjacent to the $72^{\circ}$ angle that forms a straight line. The sum of angles on a straight line is $180^{\circ}$.

Let this angle be $x$.

So, $x + 72^{\circ} = 180^{\circ}$.

Subtracting $72^{\circ}$ from both sides gives $x = 180^{\circ} - 72^{\circ} = 108^{\circ}$.

The $108^{\circ}$ angle we just found is vertically opposite to the angle formed by angle $a$ and the right angle. Vertically opposite angles are equal. Therefore, the angle formed by angle $a$ and the right angle is also $108^{\circ}$. We have:

$a + 90^{\circ} = 108^{\circ}$.

Subtracting $90^{\circ}$ from both sides gives $a = 108^{\circ} - 90^{\circ} = 18^{\circ}$.

3. Final Answer

The size of angle $a$ is $18^{\circ}$.