1. The problem states that angles 1 and 2 are supplementary. 2. Supplementary angles are two angles whose measures add up to 180 degrees. 3. The formula for supplementary angles is: $$m\angle 1 + m\angle 2 = 180^\circ$$ 4. This means the sum of the measures of angle 1 and angle 2 must equal 180 degrees. 5. Among the given options, the correct equation representing supplementary angles is: $$m\angle 1 + m\angle 2 = 180^\circ$$ 6. Therefore, the answer is the third option: $m\angle 1 + m\angle 2 = 180^\circ$.