An angle is three times its complementary angle. What is the measure of this angle in degrees?

Introduction / Context:
This question checks your understanding of complementary angles and basic linear equations. Complementary angles are two angles whose measures add up to 90 degrees. When one angle is given in terms of the other, you can set up a simple equation and solve to find the actual measure of the angle.

Given Data / Assumptions:

• Let the angle be A degrees.
• The complement of A is 90° - A.
• The problem states that A is three times its complementary angle.

Concept / Approach:
Translate the English statement into an algebraic equation using the fact that the complement of A is 90° - A. If A is three times its complement, then A = 3(90° - A). This forms a linear equation that can be solved systematically for A. Once A is known, we can directly state its measure.

Step-by-Step Solution:

Verification / Alternative check:
If A = 67.5°, then its complement is 90° - 67.5° = 22.5°. Check the condition: A should be three times its complement. Three times 22.5° is 67.5°, which matches the angle. This confirms that the calculated value is correct and consistent with the given relationship.

Why Other Options Are Wrong:

Common Pitfalls:
A frequent error is to write the relationship the wrong way, for example 90° - A = 3A instead of A = 3(90° - A) or vice versa. However, both forms actually simplify to the same equation if handled correctly. Another mistake is forgetting that complementary angles must sum to 90°, not 180° which corresponds to supplementary angles.

Final Answer:
67.5°