Final answer:
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:
- Multiply out the right-hand side: x = 360 - 4x + 5.
- Bring all x terms to one side: x + 4x = 360 + 5.
- Combine like terms: 5x = 365.
- Finally, divide both sides by 5: x = 73 degrees.
Therefore, the measure of the angle is 73 degrees.