Question

Two supplementary angles are in the ratio of 7:5.Find them.

Answer 1

let one angle be 7x and another be 5x where x is a common multiple

now 7x + 5x = 180

12x = 180

x= 180/12

x= 15

therefore one angle is 7x = 7×15=105°

another angle is 5x = 5×15=75°

Answer 2

The angles are 105° , 75°

Given :

Two supplementary angles are in the ratio of 7 : 5

To find :

The angles

Solution :

Step 1 of 3 :

Assume the angles

Here it is given that two supplementary angles are in the ratio of 7 : 5

Let the angles are 7x and 5x

Step 2 of 3 :

Form the equation

We know that two angles are said to be supplementary if sum of the angles is 180°

By the given condition

7x + 5x = 180°

Step 3 of 3 :

Find the angles

7x + 5x = 180°

⇒ 12x = 180°

⇒ x = 180°/12

⇒ x = 15°

Thus we get

First angle = 7x = 7 × 15° = 105°

Second angle = 5x = 5 × 15° = 75°

The angles are 105° , 75°

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