Final answer:
The measure of angle ZA, mZA, when ZA and ZB are complementary angles, with the given expressions for mZA and mZB, is found to be 70 degrees.
Step-by-step explanation:
If ZA and ZB are complementary angles, this means that when you add the measures of these two angles together, they should sum up to 90 degrees. Given that the measure of angle ZA, mZA, is represented by the expression (12x + 10)°, and the measure of angle ZB, mZB, is represented by the expression (5x – 5)°, we can set up an equation to reflect the fact that they are complementary angles:
mZA + mZB = 90°
(12x + 10)° + (5x – 5)° = 90°
Now, we solve for x:
12x + 10 + 5x - 5 = 90
17x + 5 = 90
17x = 85
x = 85 / 17
x = 5
Now, we find mZA by substituting x back into the expression for mZA:
mZA = (12x + 10)° = (12(5) + 10)°
mZA = (60 + 10)°
mZA = 70°
Therefore, the measure of angle ZA, mZA, is 70 degrees.