Final answer:
The measure of ∠A is found by solution of a linear equation formed by setting the sum of measures of ∠A and ∠B equal to 90°. By solving the equation, we find that the measure of ∠A is 16°.
Step-by-step explanation:
Given that ∠A and ∠B are complementary angles, their measures add up to 90°. Therefore, the equation is (x - 15)° + (3x - 19)° = 90°.
Combine like terms to get 4x - 34 = 90°. Add 34 to both sides to get 4x = 124. Divide both sides by 4 to solve for x, which is 31. Substituting x=31 into the equation for m∠A gives m∠A = (31 - 15)° = 16°. So, the measure of ∠A is 16°.
Learn more about Complementary Angles