The problem asks us to find the values of angles $a$ and $b$ in a triangle, given that one exterior angle is $276^{\circ}$ and one interior angle is $72^{\circ}$.

1. Problem Description

The problem asks us to find the values of angles $a$ and $b$ in a triangle, given that one exterior angle is $276^{\circ}$ and one interior angle is $72^{\circ}$.

2. Solution Steps

First, we need to find the interior angle $a$ corresponding to the exterior angle of $276^{\circ}$. The sum of an interior angle and its corresponding exterior angle is $360^{\circ}$ if it is a full circle. In this case the sum of an interior angle and it's linear exterior angle is $180^\circ$. Since the provided exterior angle is greater than $180^\circ$, the reference angle is not along a straight line. The interior angle $a$ and the given exterior angle of $276^\circ$ sum to $360^{\circ}$.

$a + 276 = 360$

$a = 360 - 276$

$a = 84^{\circ}$

Now we know two angles of the triangle: $72^{\circ}$ and $84^{\circ}$. The sum of the angles in a triangle is $180^{\circ}$. Therefore, we can find angle $b$ by subtracting the other two angles from $180^{\circ}$.

$72 + 84 + b = 180$

$156 + b = 180$

$b = 180 - 156$

$b = 24^{\circ}$

3. Final Answer

$a = 84^{\circ}$

$b = 24^{\circ}$