Answer:
[tex]\angle 4=160^{\circ}, \angle 6=20^{\circ}[/tex]
Step-by-step explanation:
Consider the below figure attached with this question.
Given information: a∥b, [tex]\angle 6=\frac{1}{8}\angle 4[/tex].
a∥b (Given)
[tex]\angle 6=\frac{1}{8}\angle 4[/tex] (Given)
Multiply both sides by 8.
[tex]8\angle 6=\angle 4[/tex] ...(1)
If a transversal line intersect two parallel lines then the same sided interior angles and are supplementary angles.
[tex]\angle 6+\angle 4=180[/tex] (Same sided interior angles)
[tex]\angle 6+8\angle 6=180[/tex] (Substitution)
[tex]9\angle 6=180[/tex]
Divide both sides by 9.
[tex]\angle 6=20[/tex]
The measure of angle 6 is 20 degree.
Substitute this value in equation (1).
[tex]8(20)=\angle 4[/tex]
[tex]160=\angle 4[/tex]
The measure of angle 4 is 160 degree.
