# THE MEASURES OF THE ANGLES OF A TRIANGLE ARE IN THE EXTENDED RATIO

## About "The measures of the angles of a triangle are in the extended ratio"

The measures of the angles of a triangle are in the extended ratio :

Here we are going to see how to find the measures of the angles of a triangle are in the extended ratio.

Let us look into some example problems to understand the above concept.

Example 1 :

The measures of the angles of a triangle are in the ratio 5 : 4 : 3. Find the angles of the triangle.

Solution :

Given that in a triangle ABC, <A : <B : <C = 5 : 4 : 3.

Let the angles of the given triangle be 5x°, 4x° and 3x°.

We know that the sum of the angles of a triangle is 180° .

5x° + 4x° + 3x°  =  180°

12x°  =  180°

x°  =  180°/12

=  15°

So, the angles of the triangle are 75°, 60° and 45°.

Example 2 :

The angles of a triangle are (x – 35)°, (x – 20)° and (x+40)°. Find the three angles.

Solution :

Sum of angles in a triangle  =  180°

x – 35 + x – 20 + x + 40  =  180

3x - 35 - 20 + 40 =  180

3x - 55 + 40  =  180

3x - 15  =  180

3x  =  180 + 15  =  195

x  =  195/3

x  =  65

(x – 35)  =  65 - 35  =  30°

x – 20  =  65 - 20  =  45°

x + 40  =  65 + 40  =  105°

Hence the given three angles are 30°, 45° and 105°

Example 3 :

The measures of the angles in a triangle are in the extended ratio 3:4:8. What are the measures of the angles?

Solution :

Let the angles of the given triangle be 3x°, 4x° and 8x°.

We know that the sum of the angles of a triangle is 180° .

3x° + 4x° + 8x°  =  180°

15x°  =  180°

x°  =  180°/15

=  12°

So, the angles of the triangle are 36°, 48° and 96°.

After having gone through the stuff given above, we hope that the students would have understood "The measures of the angles of a triangle are in the extended ratio".

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