Question

The two complementary angles are in the ratio 1:5 .Find the measures of the angles

Answer 1

Let the two angles be x and 5x

The sum of complementary angles = 90°

x + 5x = 90°

6x = 90°

$x = \frac {90}{6}$

x = 15°

Ans. The two angles are 15° and 5 × 15 = 75°

Answer 2

Let the ratio be taken as x...
Hence the ratio 1:5 can be take as 1x or x and 5x

Complementary angles are the angles whose sum adds correctly to 90°

x+5x = 90°
6x = 90°
x = 90/6
x = 15°

Hence the angles are x and 5x
That is 15° and 5×15° = 75°

VERIFICATION...

15°+75° = 90°