Since angles ∠1 and ∠2 are supplementary, their measures add up to 180°. Given that \( m∠1 = 77° \) and letting \( m∠2 = x \), we can set up the equation:
\[ x + 77° = 180° \]
To solve for \( x \), you can subtract 77° from both sides of the equation:
\[ x = 180° - 77° \]
Now, you can calculate the value:
\[ x = 103° \]
Thus, the equation you would write to solve for \( m∠2 \) is:
\[ x + 77° = 180° \]