Question

The difference of two complementary angles is 30°. Then, the angles are ______.

Options

• 60°, 30°

• 70°, 40°

• 20°, 50°

• 105°, 75°

Answer 1

The difference of two complementary angles is 30°. Then, the angles are 60°, 30°.

Explanation:

Let one of the angles be x.

Since, the difference between the two angles is 30°, then the other angle will be (x – 30°).

Also, the two angles are complementary, so their sum is equal to 90°.

∴ x + (x – 30°) = 90°

⇒ x + x – 30° = 90°

⇒ 2x = 90° + 30°

⇒ 2x = 120°

⇒ x = `120^circ/2`

⇒ x = 60°

∴ Required angles are 60° and (60° – 30°), i.e. 60°and 30°.