Answer:
m∠1 = 100°, m∠2 = 80°
Step-by-step explanation:
We know: Supplementary angles add up to 180°.
Therefore
m∠1 + m∠2 = 180° → m∠2 = 180° - m∠1 (*)
We have
[tex]m\angle1:m\angle2=5:4\to\dfrac{m\angle1}{m\angle2}=\dfrac{5}{4}[/tex]
Substitute (*):
[tex]\dfrac{m\angle1}{180^o-m\angle1}=\dfrac{5}{4}[/tex] cross multiply
[tex]4m\angle1=5(180^o-m\angle1)[/tex] use the distributive property
[tex]4m\angle1=(5)(180^o)+(5)(-m\angle1)[/tex]
[tex]4m\angle1=900^o-5m\angle1[/tex] add 5m∠1 to both sides
[tex]9m\angle1=900^o[/tex] divide both sides by 9
[tex]m\angle1=100^o\to m\angle2=180^o-100^o=80^o[/tex]
