Answer: In a parallelogram, opposite angles are congruent. So we know that angle A is congruent to angle C. Let's call the measure of angle A "y".
Therefore, we have:
angle A = y
angle B = 3x + 36
angle C = y (because opposite angles in a parallelogram are congruent)
angle D = 6x - 6
The sum of the measures of the angles in a parallelogram is 360 degrees. So we can write an equation:
angle A + angle B + angle C + angle D = 360
Substituting in the values we know:
y + (3x + 36) + y + (6x - 6) = 360
Simplifying:
2y + 9x + 30 = 360
2y + 9x = 330
Now we have an equation with two variables. But we also know that angle A and angle C are congruent, so y = angle A = angle C. Substituting this into the equation above:
2(angle A) + 9x = 330
2(angle A) = 330 - 9x
angle A = (330 - 9x)/2
Therefore, the measure of angle A is (330 - 9x)/2.
Explanation: