Question

The ratio of two complementary angles is 1:2, determine the ratio of the larger angle to its supplementary angle. Note, two angles are complementary when they add up to 90 degrees and are supplementary when they add up to 180 degrees.​

Answer 1

Step-by-step explanation:

let the angles be 1x , 2x

Complementary angles are equal to 90°

so 1x + 2x = 90°

3x = 90°

x = 90/3

x = 30°

2x = 60°

Supplementary angles are equal to 180°

if one angle is 60° then other will be 120° ( larger one )

Answer 2

SOLUTION

GIVEN

The ratio of two complementary angles is 1 : 2

TO DETERMINE

The ratio of the larger angle to its supplementary angle.

EVALUATION

Here it is given that the ratio of two complementary angles is 1 : 2

Let the angles are x and 2x

We know that two angles are said to be complementary if sum of angles = 90°

So we have

x + 2x = 90°

⇒ 3x = 90°

⇒ x = 30°

So the angles are 30° & 60°

Larger angle = 60°

Again two angles are said to be supplementary if sum of angles = 180°

Supplementary angle of Larger angle

= Supplementary angle of 60°

= 180° - 60°

= 120°

Hence the required ratio

= 60° : 120°

= 60 : 120

= 1 : 2

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