Question

the ratio of two complementary angles is 4:5 find these angles and ratio of their supplementary angles.

Answer 1

Answer:

Let the first angle be 4x

Second angle = 5x

According to question

4x+5x = 90

=> 9x = 90

=> x = 10

First angle = 40°

Second angle = 50°

Now,

Supplement of first angle = 180 - 40 = 140°

Supplement of second angle = 180 - 50 = 130°

Ratio of Supplement = 140:130 = 14 : 13

Answer 2

Given :

• The ratio of two complementary angles is 4 : 5.

To find :

• The angles and ratio of their supplementary angles.

Step-by-step explanation :

1st Case :

As we know that,

Complementary angles = 90°

The ratio is 4:5. [Given]

Now,

Let the ratio of two complementary angles be 4x and 5x.

As We know that,

Sum of Complementary angles = 90°

According to the question :

➮ 4x + 5x = 90°

➮ 9x = 90°

➮ x = 90/9

➮ x = 10°

Therefore, We get the value of x = 10°

Hence,

Measure of 1st angle = 4x ➮ 4 × 10 = 40°

Measure of 2nd angle = 5x ➮ 5 × 10 = 50°

2nd Case :

We know that,

Supplementary angle = 180°

Value of 1st Supplement angle = 180 - 40 = 140°

Value of 2nd Supplement angle = 180 - 50 = 130°

Now,

Ratio supplementary angle = Value of 1st Supplement angle / Value of 2nd Supplement angle.

Substituting the values, we get

= 140/130

= 14/13.

Therefore, The Ratio of the Supplementary angles = 14 : 13.