Answer:
Here, we use the law of alternate interior angles. <3 and <6 are are alternat.e interior angles, meaning they have the same measure. We can solve x by using this equation:
3x-2=34
Add 2 to both sides
3x-2+2=34+2
3x=36
Divide both sides by 3
3x/3=36/3
x=12
2. Here, we use the law of consecutive interior angles. <4 and <6 are consecutive interior angles, meaning that the sum of their measures is equal to 180 degrees. We can solve x by using this equation:
-2x+20+6x+20=180
4x+40=180
Subtract both sides by 40
4x+40-40=180-40
4x=140
Divide both sides by 4
4x/4=140/4
x=35
3. Here, we use the law of alternate exterior angles. <7 and <2 are alternate exterior angles, meaning that their measures are the same. We can solve x by using this equation:
4x+3=x+15
Subtract both sides by 3
4x+3-3=x+15-3
4x=x+12
Subtract both sides by x
4x-x=x+12-x
3x=12
Divide both sides by 3
3x/3=12/3
x=4
4. Here, we use the law of alternate interior angles (again). <4 and <5 are alternate interior angles, meaning that they have the same measure. We can solve x by using this equation:
5x-3=3x+17
Add both sides by 3
5x-3+3=3x+17+3
5x=3x+20
Subtract both sides by 3x
5x-3x=3x+20-3x
2x=20
Divide both sides by 2
2x/2=20/2
x=10
5. Here, we use the law of consecutive interior angles (again). <3 and <5 are consecutive interior angles, meaning that the sum of their measures is equal to 180 degrees. We can solve x by using this equation:
5x-6+19=180
5x+13=180
Subtract both sides b.y 13
5x+13-13=180-13
5x=167
Divide b.oth sides by 5
5x/5=167/5
x=33.4
I hope this helps!
Explanation: