Final answer:
After solving the equation for vertical angles, the measure of angle 1 is found to be 127°, which does not match any of the provided answer choices, indicating a possible error in the question or the options.
Step-by-step explanation:
The student's question involves finding the measure of vertical angles. Given that m∠1 and m∠2 are vertical angles, which means they are equal, we can set the expressions for their measures equal to each other: 5x + 12 = 6x – 11. Solving for x, we subtract 5x from both sides to get x on one side: 12 = x - 11. Then, adding 11 to both sides, we get x = 23. Now that we have the value of x, we can find m∠1 by substituting x back into the expression for m∠1: m∠1 = 5(23) + 12 which is 115 + 12, so m∠1 = 127°. However, since none of the provided options (a, b, c, d) match this result, and assuming the student is expected to choose one of these options, there might be a mistake in the given choices or in the original equations for the angles.