Question

How to solve Parallel lines with transversal?

Answer 1

6) Since these are parallel lines with a transversal, angle 9x+2 is equal to the bottom right exterior angle. The bottom right exterior angle and 4x+22 are equivalent to 180° because their angles are on a line. Lines=180°.

180°=(9x+2)+(4x+22)
180=13x+24
Subtract 24 from both sides
156=13x
Divide both sides by 13
12= x

Substitute x=12 to solve both equations

9x+2=9(12)+2= 110°
4x+22=4(12)+22= 70°

7) 180=(16x-6)+(16x-6)
180= 32x-12
Add 12 to both sides
192=32x
Divide both sides by 32
6=x

16x-6= 16(6)-6= 90°
16x-6= 16(6)-6= 90°

8) These are alternate exterior angles and are equivalent to each other.

14x-10=12x+10
Add 10 to both sides
14x= 12x+20
Subtract 12x from both sides
2x= 20
Divide both sides by 2
x=10

14x-10=14(10)-10= 130°
12x+10=12(10)+10=130°

9) 180=(x+134)+(x+64)
180=2x+198
Subtract 198 from both sides
-18=2x
Divide both sides by 2
-9=x

x+134= (-9)+134=125°
x+64= (-9)+64=55°

Notice that answers to 6, 7 and 9 add up to 180° (degrees in a line). And the answers to 8 are equal to each other.

I hope this helps! Good luck! :)

Answer 2

Same-side interior angles are supplementary, so add to 180°.

Opposite side exterior angles are equal.

Solve these by using the appropriate relation with the given expressions.

9) (x +134) +(x +64) = 180
.. 2x +198 = 180
.. x = (180 -198)/2 = -9
The angles are 125° (top) and 55° (bottom).