Question

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

Answer 1

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

$m\angle1:m\angle2=5:4\to\dfrac{m\angle1}{m\angle2}=\dfrac{5}{4}$

Substitute (*):

$\dfrac{m\angle1}{180^o-m\angle1}=\dfrac{5}{4}$           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

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