Final answer:
The measure of angle m1 is 41 degrees.
Step-by-step explanation:
Vertical angles are pairs of angles formed by two intersecting lines. They are always congruent, which means they have equal measures.
In this case, we are given that m∓1 = 6x + 11 and m2 = 10x - 9. Since vertical angles are congruent, we can set their measures equal to each other.
6x + 11 = 10x - 9
Now, we can solve for x:
11 + 9 = 10x - 6x
20 = 4x
x = 5
Substitute the value of x back into either equation to find the measure of m1:
m1 = 6x + 11
m1 = 6(5) + 11
m1 = 30 + 11
m1 = 41
Therefore, the measure of m1 is 41 degrees.