Final answer:
To find the value of the variable, we can set up an equation and solve for x. Substituting the given expressions for m25 and m_1, we obtain 5x + 38 = 2x + 44. Solving for x gives us x = 6. Substituting this value back into the expressions for m25 and m_1, we find that m25 = 68 and m_1 = 56. Therefore, the value of the variable is 10.
Step-by-step explanation:
To find the value of the variable, we need to set up an equation using the given information. We are told that m || 1.m_1, which means that the angle formed by m and 1.m_1 is equal to the angle formed by 1.m_1 and the line parallel to m. We are also given that m25 = 5x + 38 and m_1 = 2x + 44. The diagram is not to scale, so we cannot rely on the visual representation of the angles. We can set up the equation m25 = m_1, since the corresponding angles are equal. Substituting the given expressions for m25 and m_1, we have 5x + 38 = 2x + 44. Solving for x, we get x = 6. Substituting this value back into the expressions for m25 and m_1, we find that m25 = 5(6) + 38 = 68 and m_1 = 2(6) + 44 = 56. Therefore, the correct answer is A. 10.