We are given a triangle with angles $54^{\circ}$ and $48^{\circ}$. We are also told that angle $q$ and angle $r$ are on a straight line. We need to find the value of angle $q$ and angle $r$.

1. Problem Description

We are given a triangle with angles $54^{\circ}$ and $48^{\circ}$. We are also told that angle $q$ and angle $r$ are on a straight line. We need to find the value of angle $q$ and angle $r$.

2. Solution Steps

a) Work out the size of angle q.

First, we can find the size of angle $q$ using the fact that the sum of angles in a triangle is $180^{\circ}$.

$54^{\circ} + 48^{\circ} + q = 180^{\circ}$

$102^{\circ} + q = 180^{\circ}$

$q = 180^{\circ} - 102^{\circ}$

$q = 78^{\circ}$

b) Work out the size of angle r.

Next, we can find the size of angle $r$ using the fact that angles on a straight line add up to $180^{\circ}$.

$q + r = 180^{\circ}$

$78^{\circ} + r = 180^{\circ}$

$r = 180^{\circ} - 78^{\circ}$

$r = 102^{\circ}$

3. Final Answer

a) $q = 78^{\circ}$

b) $r = 102^{\circ}$