Final answer:
The measure of the angle is approximately 1.4° and the measure of its complementary angle is approximately 88.6°.
Step-by-step explanation:
Let's represent the measure of the angle as x.
The measure of the complementary angle can be represented as 90 - x (since the sum of complementary angles is 90°).
According to the problem, the angle measures 85.8° less than the measure of its complementary angle:
x = (90 - x) - 85.8
Simplifying the equation:
2x = 90 - x - 85.8
3x = 90 - 85.8
3x = 4.2
x = 4.2 / 3
x ≈ 1.4
So, the measure of the angle is approximately 1.4° and the measure of its complementary angle is approximately 88.6°.