We are asked to find the size of angle $a$ in the given diagram.

1. Problem Description

We are asked to find the size of angle $a$ in the given diagram.

2. Solution Steps

First, we can see that the $72^{\circ}$ angle and the right angle ($90^{\circ}$) form part of the angles on a straight line.

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

So, let the angle between the $72^{\circ}$ angle and angle $a$ be $x$. Then we have:

$72^{\circ} + 90^{\circ} + x = 180^{\circ}$

$162^{\circ} + x = 180^{\circ}$

$x = 180^{\circ} - 162^{\circ}$

$x = 18^{\circ}$

Angle $a$ and $x$ also form a straight line, thus:

$a + x = 180^{\circ}$

$a + 18^{\circ} = 180^{\circ}$

$a = 180^{\circ} - 18^{\circ}$

$a = 162^{\circ}$

3. Final Answer

The size of angle $a$ is $162^{\circ}$.