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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!

Step-by-step explanation:

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

step-by-step explanation:

given   that triangle lno is congruent to triangle lnm.

we have to fill up the blanks in the given question.

according to above order of congruency   kept in mind we can say that

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

ln ≅ ln due to common in both.

hence, by sas congruency,

the side angle side rule   states that if two sides and the included angle of one triangle are congruent to another triangle, then these two triangles are congruent.