Final answer:
To solve for x given alternate interior angles (7x - 13) and (5x + 21), we set them equal due to their property of equality when lines are parallel, simplify the equation, and find x = 17.
Step-by-step explanation:
Finding the Value of x
To find the value of x when given that alternate interior angles are (7x - 13) and (5x + 21), we need to set the expressions equal to each other because alternate interior angles are equal when lines are parallel. The equation becomes 7x - 13 = 5x + 21. Solving for x, we subtract 5x from both sides of the equation, resulting in 2x - 13 = 21. Then we add 13 to both sides, which gives 2x = 34. Finally, dividing both sides by 2 finds that x = 17.
Step-by-Step Solution
Set the alternate interior angles equal: 7x - 13 = 5x + 21
Subtract 5x from both sides: 2x - 13 = 21
Add 13 to both sides: 2x = 34
Divide both sides by 2: x = 17