Answer:
The measure of the first angle is 87.7 degrees, and the measure of its complementary angle is approximately 2.3 degrees.
Explanation:
Let's represent the measure of the first angle as x degrees.
According to the given information, the measure of the second angle (its complementary angle) is 85.4° less than the measure of the first angle. Therefore, the measure of the second angle is (x - 85.4) degrees.
Since the two angles are complementary, their sum is 90 degrees.
So, we can set up the equation:
x + (x - 85.4) = 90
Now, combine like terms:
2x - 85.4 = 90
Next, isolate the variable "x" by adding 85.4 to both sides of the equation:
2x = 90 + 85.4
2x = 175.4
Finally, divide both sides by 2 to solve for "x":
x = 175.4 / 2
x = 87.7
The measure of the first angle is 87.7 degrees.
Now, to find the measure of the second angle (its complementary angle), subtract 85.4 from x:
Second angle = 87.7 - 85.4
Second angle ≈ 2.3 degrees
So, the measure of the first angle is 87.7 degrees, and the measure of its complementary angle is approximately 2.3 degrees.