Question

An angle measures 5 degrees more than 4 times its complement. Find the measure of the angle.

Answer 1

The measure of the angle, which is 5 degrees more than 4 times its complement, is solved by setting up and solving the algebraic equation. The angle is found to be 73 degrees.

Step-by-step explanation:

To find the measure of the angle in question, we use a combination of algebra and our knowledge of complementary angles. Remember that complementary angles add up to 90 degrees. Let's let x represent the measure of our unknown angle. If the angle is 5 degrees more than 4 times its complement, we can express this as the equation x = 4(90 - x) + 5.

Let's solve the equation step by step:

1. Multiply out the right-hand side: x = 360 - 4x + 5.
2. Bring all x terms to one side: x + 4x = 360 + 5.
3. Combine like terms: 5x = 365.
4. Finally, divide both sides by 5: x = 73 degrees.

Therefore, the measure of the angle is 73 degrees.