The difference of two angles is $${1^ \circ };\,$$ the circular measure of their sum is 1. What is the smaller angle in circular measure ?

Solution :
Let the angles are $$\alpha $$ and $$\beta ,$$ then $$\alpha - \beta = {1^ \circ }$$
$$ \Rightarrow \alpha - \beta = \frac{\pi }{{{{180}^ \circ }}}$$    is circular measure $$\,\,\,\,.....\left( {\text{i}} \right)$$
As given, $$\alpha + \beta = 1\,\,\,\,\,.....\left( {{\text{ii}}} \right)$$
On solving Eqs. (i) and (ii), we get,
$$\alpha = \frac{1}{2}\left[ {1 + \frac{\pi }{{{{180}^ \circ }}}} \right]{\text{ and }}\beta = \frac{1}{2}\left[ {1 - \frac{\pi }{{{{180}^ \circ }}}} \right]$$
$$\beta $$ is the smaller angle.
Hence, smaller angle $$ = \frac{1}{2}\left[ {1 - \frac{\pi }{{{{180}^ \circ }}}} \right]$$