Question

An angle measures 85.8° less than the measure of its complementary angle. What is the measure of each angle?

Answer 1

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°.