The complement of an angle exceeds the angle by 60°. Find the angle.
Aptitude
Plane Geometry
Difficulty: Easy
Choose an option
-
A25°
-
B30°
-
C15°
-
D35°
Answer
Correct Answer: 15°
Explanation
Introduction / Context:A complement is defined as 90° minus the angle. If the complement is 60° larger than the angle itself, set up and solve a linear equation.
Given Data / Assumptions:
- Let the angle be x°.
- Complement = 90° − x.
- Given: (90° − x) = x + 60°.
Concept / Approach:Rearrange to isolate x and compute the measure directly.
Step-by-Step Solution:
90 − x = x + 6090 − 60 = x + x30 = 2x ⇒ x = 15°Verification / Alternative check:Complement = 75°; 75° exceeds 15° by 60°, satisfying the condition.
Why Other Options Are Wrong:25°, 30°, 35° fail the relation (90 − x) − x = 60.
Common Pitfalls:Confusing complement with supplement; sign mistakes moving terms across the equality.
Final Answer:15°