Answer:
α = 72.5°
β = 17.5°
Step-by-step explanation:
Let's call the two angles α and β.
Complementary angles are those that add up to 90 degrees.
α + β = 90° [1]
The difference of two complementary angles is 55 degrees.
α - β = 55° [2]
Let's add [1] and [2] side to side.
α + β + α - β = 90° + 55°
2α = 145°
α = 72.5°
From [1],
α + β = 90°
72.5°C + β = 90°
β = 17.5°
