Question

The smaller of two complementary angles falls short of the larger by 12°
Find the angles.

Answer 1

Answer:

The angles are 39° and 51°

Answer 2

The larger angle = 51°  and the smaller angle = 39°

Step-by-step explanation:

Let the larger angle = x and the smaller angle = (x - 12°)

To find, the two complementary angles = ?

We know that,

The sum of two complementary angles = 90°

∴ x + (x - 12°) = 90°

⇒ x + x - 12° = 90°

⇒ 2x - 12° = 90°

⇒ 2x = 90° + 12° = 102°

⇒ x = $\dfrac{102}{2}$ = 51°

∴ x - 12° =51°  - 12° = 39°

∴ The larger angle = 51°  and

The smaller angle = 39°