Final answer:
Using the corresponding angles postulate, the equations m∠2 = 9x + 2 and m∠10 = 15x - 2 are set equal to each other, resulting in finding the value of x to be 2/3.
Step-by-step explanation:
To find the value of x when given that lines s are parallel to t and line c is parallel to d, and the equations m∠2 = 9x + 2 and m∠10 = 15x - 2, we need to use the corresponding angles postulate which states that corresponding angles are congruent when two lines are parallel and cut by a transversal. Since m∠2 and m∠10 are corresponding angles, they are equal. Therefore, we can set the two equations equal to each other to find the value of x: 9x + 2 = 15x - 2.
Solving for x involves subtracting 9x from both sides, giving us 2 = 6x - 2, and then adding 2 to both sides to get 4 = 6x. Finally, divide both sides by 6 to obtain x = 4/6, which simplifies to x = 2/3.