Complementary angles are two angles whose measures add up to 90 degrees. Given that \( m\angle 5 = 39^\circ \), we can set up the following equation to solve for \( m\angle 6 \):
\[ m\angle 6 + 39 = 90 \]
This equation is correct. To isolate \( m\angle 6 \), you would subtract 39 from both sides:
\[ m\angle 6 = 90 - 39 \]
Thus, the correct equation to use is:
\[ m\angle 6 + 39 = 90 \]
The other options provided are incorrect because:
- \( m\angle 6 + 39 = 180 \) is incorrect because complementary angles must sum to 90, not 180.
- \( m\angle 6 = 180 - 39 \) is also incorrect for the same reason.
- \( m\angle 6 = 39 \) is incorrect because it does not take into account the measure of angle 5.
So the correct option to write would be:
\[ m\angle 6 + 39 = 90 \]