Complement of an angle in degrees and minutes: Find the complement of 30° 20′.

Introduction / Context:Complementary angles sum to 90°. Subtract the given angle from 90° taking care with minutes conversion (60′ = 1°).

Given Data / Assumptions:

• Angle = 30° 20′.
• Complement = 90° 00′ − 30° 20′.

Concept / Approach:Borrow 1° as 60′ if needed, then subtract degrees and minutes separately.

Step-by-Step Solution:90° 00′ − 30° 20′ = 59° 40′

Verification / Alternative check:59°40′ + 30°20′ = 90°00′, confirming complementarity.

Why Other Options Are Wrong:69°40′ exceeds 90° − 30°; 35°80′ uses an invalid minute format (80′ ≡ 1°20′).

Common Pitfalls:Forgetting to convert 60′ to 1° when minutes exceed 59.

Final Answer:59°40′