Question

name: parallel lines practice date: 20) 75° 11x - 2 22) x + 139 132° 23) -1 + 14x 12x + 17 25) x + 96 x + 96 27) 6x 5x + 10 28) x + 109 x + 89

Explanation:

Step1: Recall angle - relationship for parallel lines

When two parallel lines are cut by a transversal, corresponding angles are equal, alternate - interior angles are equal, and same - side interior angles are supplementary.

Step2: Solve problem 20

Since the angles are corresponding angles, we set up the equation $11x - 2=75$.
Add 2 to both sides: $11x=75 + 2=77$.
Divide both sides by 11: $x=\frac{77}{11}=7$.

Step3: Solve problem 22

The angles are same - side interior angles, so they are supplementary. The equation is $(x + 139)+132 = 180$.
First, simplify the left - hand side: $x+139 + 132=x + 271$.
Then, solve for $x$: $x=180−271=-91$. But since angles are non - negative in this context, we may have misidentified the angle relationship. They are actually alternate exterior angles, so $x + 139=132$, and $x=132 - 139=-7$.

Step4: Solve problem 23

The angles are alternate interior angles, so $-1 + 14x=12x+17$.
Subtract $12x$ from both sides: $-1 + 14x-12x=12x + 17-12x$, which gives $2x-1 = 17$.
Add 1 to both sides: $2x=17 + 1=18$.
Divide both sides by 2: $x = 9$.

Step5: Solve problem 25

The angles are corresponding angles, and since they are equal, the equation $x + 96=x + 96$ is always true for all real values of $x$. This indicates that the lines are parallel for any value of $x$.

Step6: Solve problem 27

The angles are corresponding angles, so $6x=5x + 10$.
Subtract $5x$ from both sides: $6x-5x=5x + 10-5x$, and $x = 10$.

Step7: Solve problem 28

The angles are same - side interior angles, so $(x + 109)+(x + 89)=180$.
Combine like terms: $2x+198 = 180$.
Subtract 198 from both sides: $2x=180 - 198=-18$.
Divide both sides by 2: $x=-9$.

Answer:

Problem 20: $x = 7$
Problem 22: $x=-7$
Problem 23: $x = 9$
Problem 25: All real $x$
Problem 27: $x = 10$
Problem 28: $x=-9$