Answer:
angle 7=100 ,angle 8=80
Explanation:
For angle 7:
By using definition of alternate interior angles:
angle 4=angle 6
Subtitute values of angles:
x+2y=3y+20
x+2y-3y=20
x-y=20.......(1)
Now by using definition of alternate opposite angles:
angle 4= angle 2
angle 2=x+2y
Angle 1 and angle 2 are the angles of straight line ,there sum will be 180.
2x+y+x+2y=180
3x+3y=180
x+y=60......(2)
Add (1) and (2):
x-y=20
x+y=60
_______
2x=80
x=40
subtitute x=40 in (2):
40+y=60
y=60-40
y=20
For angle 7:
By using definition of alternate exterior angle:
angle 1=angle 7
angle 7=2x+y
subtitute x and y:
angle 7=2(40)+20
=100
For angle 8:
By using definition of alternate opposite angle:
angle 8=angle 6
angle 8= 3y+20
angle 8=3(20)+20
=80