Final answer:
By solving the equation for complementary angles, we find that the measure of angle ZA (m_A) equals 21 degrees.
Step-by-step explanation:
To find the measure of angle ZA (mA), we are given that angles ZA and ZB are complementary angles. This means the sum of mA and mZB is 90 degrees. The problem states that mA = (x – 21)° and mZB = (2x – 15)°. Since they are complementary:
mA + mZB = 90° \ (x – 21)° + (2x – 15)° = 90° \ 3x – 36 = 90 \ 3x = 126 \ x = 42
Now, we can find mA by plugging x back into its equation:
mA = (42 – 21)° = 21 degrees.