Answer:
22.5° and 157.5°
Step-by-step explanation:
Supplementary angles total 180°.
Therefore, ∠1 plus ∠2 equals 180°.
If ∠1 = x, then ∠2 = 7x, since its measure is "7 times the measure of its supplementary angle."
Solving for x:
[tex]\angle{1}+\angle{2}=180^{\circ}\\x+7x=180^{\circ}\\8x=180^{\circ}\\x=22.5^{\circ}[/tex]
Therefore, ∠1 = 22.5° and ∠2 = 7(22.5°) = 157.5°.
To verify, we check that both angles total 180°:
22.5° + 157.5° = 180°
Check.
