Final answer:
The measure of ∠A in trapezoid ABCD is 57 degrees. This is found by establishing the supplementary relationship between ∠A and ∠D, solving for x, and substituting back to find m∠A.
Step-by-step explanation:
To find the measure of ∠A in trapezoid ABCD, given that AB ∥ DC and the measures of the angles at A and D are m∠A = 2x + 7 and m∠D = 5x - 2, it is important to know that in a trapezoid, the angles on the same side of the legs are supplementary. Therefore, we can set up the equation:
m∠A + m∠D = 180 degrees
This equation becomes:
2x + 7 + 5x - 2 = 180
Simplifying gives:
7x + 5 = 180
Subtracting 5 from both sides:
7x = 175
Dividing both sides by 7:
x = 25
Now, substituting x into the expression for m∠A:
m∠A = 2(25) + 7 = 50 + 7 = 57 degrees
Thus, the measure of ∠A in trapezoid ABCD is 57 degrees.