Final answer:
To find the measure of angle m∠1, we need to use the given information that m and n are parallel lines and m∠1 = 4x - 6. By setting up and solving an equation, we find that the measure of angle m∠1 is 86 degrees.
Step-by-step explanation:
To find the measure of angle m∠1, we need to use the given information that m and n are parallel lines and m∠1 = 4x - 6. Since m and n are parallel lines, the corresponding angles formed by the transversal line n are congruent. Therefore, m∠1 is equal to m∠7 which is given as 2x + 40. So we can set up an equation:
4x - 6 = 2x + 40
Now, let's solve for x:
4x - 2x = 40 + 6
2x = 46
x = 23
Now substitute the value of x in m∠1 = 4x - 6:
m∠1 = 4(23) - 6
m∠1 = 92 - 6
m∠1 = 86
Therefore, the measure of angle m∠1 is 86 degrees. So, the correct answer is D. 40 degrees.