Question

1. complete the sentence related to the diagram below. solve for x. if 2 parallel lines are cut by a transversal, then angles are -1 + 14x 12x + 17 23. complete the sentence related to the diagram below. solve for x. if 2 parallel lines are cut by a transversal, then angles are 60° 8x - 4 24. complete the sentence related to the diagram below. solve for x. if 2 parallel lines are cut by a transversal, then angles are 20x + 5 24x - 1 25. complete the sentence related to the diagram below. solve for x. if 2 parallel lines are cut by a transversal, then angles are 6x 5x + 10

Explanation:

Step1: Identify angle - relationship

When two parallel lines are cut by a transversal, corresponding angles are equal. In problem 22, we assume the two given angles are corresponding. So we set up the equation $- 1+14x=12x + 17$.

Step2: Solve the equation for $x$

Subtract $12x$ from both sides: $-1+14x-12x=12x + 17-12x$, which simplifies to $-1 + 2x=17$. Then add 1 to both sides: $2x=17 + 1=18$. Divide both sides by 2: $x = 9$.

Step3: For problem 23

Assume the angles are corresponding. Set up the equation $8x-4=60$. Add 4 to both sides: $8x=60 + 4=64$. Divide both sides by 8: $x = 8$.

Step4: For problem 24

Assume the angles are corresponding. Set up the equation $20x+5=24x - 1$. Subtract $20x$ from both sides: $5=24x-1-20x$, which simplifies to $5 = 4x-1$. Add 1 to both sides: $4x=5 + 1=6$. Divide both sides by 4: $x=\frac{6}{4}=\frac{3}{2}=1.5$.

Step5: For problem 25

Assume the angles are corresponding. Set up the equation $6x=5x + 10$. Subtract $5x$ from both sides: $6x-5x=5x + 10-5x$. So $x = 10$.

Answer:

1. $x = 9$
2. $x = 8$
3. $x = 1.5$
4. $x = 10$