Final answer:
To find m1 in a parallelogram with given expressions for opposite angles, we equate those expressions, solve for 'x', and then substitute 'x' back to find the measure of m1, which turns out to be 16 degrees.
Step-by-step explanation:
To find the measure of angle m1 in the parallelogram given that m/2 is 4x-20 and m/24 is 3x-11, we need to use properties of parallelograms. In a parallelogram, opposite angles are equal. Therefore, m1 = m/24 because they are opposite angles. We set up an equation to find the value of 'x' first by equating the expressions for m/2 with m/24:
m/2 = m/24
4x - 20 = 3x - 11
Solving for 'x', we get:
x = 9
Now, we substitute 'x' back into the expression for either m/2 or m/24 to find the measure of m1:
m1 = 3x - 11
m1 = 3(9) - 11
Therefore, the measure of angle m1 is:
m1 = 27 - 11
m1 = 16 degrees.