Answer:
The angles are : 85°,85°,70° and 70°
Step-by-step explanation:
to find the measure of each labeled angle.
For the given parallel lines:
[tex]5x\° =(3x+34)\°[/tex] [ exterior alternate angles of a traversal between parallel lines have same measure.]
Solving for [tex]x[/tex]
Subtracting both sides by [tex]3x[/tex]
[tex]5x-3x=3x-3x+34[/tex]
[tex]2x=34[/tex]
Dividing both sides by 2.
[tex]\frac{2x}{2}=\frac{34}{2}[/tex]
∴ [tex]x=17\°[/tex]
Measure of angle =[tex]5\times 17\°=85\°[/tex]
[tex]2y\° =(3y-35)\°[/tex] [corresponding angles of traversal between parallel lines have same measure.]
Solving for [tex]y[/tex]
Subtracting both sides by [tex]3y[/tex]
[tex]2y-3y=3y-3y-35[/tex]
[tex]-y=-35[/tex]
Dividing both sides by -1.
[tex]\frac{-y}{-1}=\frac{-35}{-1}[/tex]
∴ [tex]y=35\°[/tex]
Measure of angle =[tex]2\times 35\°=70\°[/tex]
