Question

Find the measures of supplementary angles 1 and 2, if: m∠1:m∠2=5:4 using statements and reasons.

Answer 1

m∠1 = 100°, m∠2 = 80°

Explanation:

We know: Supplementary angles add up to 180°.

Therefore

m∠1 + m∠2 = 180° → m∠2 = 180° - m∠1 (*)

We have

`m\angle1:m\angle2=5:4\to(m\angle1)/(m\angle2)=(5)/(4)`

Substitute (*):

`(m\angle1)/(180^o-m\angle1)=(5)/(4)` cross multiply

`4m\angle1=5(180^o-m\angle1)` use the distributive property

`4m\angle1=(5)(180^o)+(5)(-m\angle1)`

`4m\angle1=900^o-5m\angle1` add 5m∠1 to both sides

`9m\angle1=900^o` divide both sides by 9

`m\angle1=100^o\to m\angle2=180^o-100^o=80^o`