Question

If the difference of two complementary angles x and y is 6°, then the product xy equals

• A. 1024
• B. 2048
• C. 2016
• D. 1729

Answer 1

The correct option is C 2016

Given that the difference of two complementary angles x and y is 6°.
Let x > y.
∴ x – y = 6° …..(i)
Since x and y are complementary angles.
∴ x + y = 90° …..(ii)
Adding (i) and (ii), we get
x – y + x + y = 6° + 90°
⇒ 2x = 96°
⇒ x = 48°
Substituting x = 48° in (ii), we get
48° + y = 90°
⇒ y = 90° – 48° = 42°
∴ x = 48° and y = 42°
⇒ xy = 48 × 42
= 2016
Hence, the correct answer is option (c).