Supplementary angles are two angles whose measures add up to 180 degrees. Given that \( m<b = 43 \), we can find \( m<a \) using the relationship:
\[ m<a + m<b = 180 \]
Substituting the known value of \( m<b \):
\[ m<a + 43 = 180 \]
To find \( m<a \), we can rearrange the equation:
\[ m<a = 180 - 43 \]
Calculating this gives:
\[ m<a = 137 \]
Thus, the value of \( m<a \) is \( \boxed{137} \).