The problem asks us to find the size of the reflex angle $BCD$ in the given diagram. The diagram shows triangle $ABD$ and triangle $ABC$. We are given that $\angle D = 33^\circ$, $\angle B = 25^\circ$, and $\angle A = 51^\circ$.

1. Problem Description

The problem asks us to find the size of the reflex angle $BCD$ in the given diagram. The diagram shows triangle $ABD$ and triangle $ABC$. We are given that $\angle D = 33^\circ$, $\angle B = 25^\circ$, and $\angle A = 51^\circ$.

2. Solution Steps

First, we need to find the angle $C$ of triangle $ABC$, i.e. $\angle BCA$. The sum of angles in triangle $ABC$ is 180 degrees. We know $\angle A = 51^\circ$ and $\angle B = 25^\circ$. Therefore, we can use the following formula:

$\angle A + \angle B + \angle BCA = 180^\circ$

Substituting the given values:

$51^\circ + 25^\circ + \angle BCA = 180^\circ$

$76^\circ + \angle BCA = 180^\circ$

$\angle BCA = 180^\circ - 76^\circ$

$\angle BCA = 104^\circ$

The reflex angle $BCD$ is the angle outside of the $104^\circ$ angle at vertex $C$. Since a full circle is $360^\circ$, the reflex angle is:

$360^\circ - \angle BCA =$ Reflex $\angle BCD$

$360^\circ - 104^\circ = 256^\circ$

3. Final Answer

The size of the reflex angle $BCD$ is $256^\circ$.