Question

three angles of a quadrilateral are in the ratio 3:4:5 .the difference of the least and the greatest of these angle is 45 degree find the all the four angles of the quadrilateral​

Answer 1

Solution :

Three angles of a quadrilateral are in the ratio 3:4:5

The difference of the least and the greatest of these angle is 45 degrees.

We have to find all the angles of the quadrilateral.

Let the angles in ratio be 3x, 4x and 5x respectively.

The sum of all angles in a quadrilateral is 360°

Therefore the 4th angle will be (360-14x)°

The difference between the least and greatest angle is 45.

3x < (360 - 14x) < 5x

5x - 3x = 45

>> 2x = 45

>> x = 22.5°

3x = 67.5

4x = 90

5x = 112.5

(360-14x) = 90

Answer : The four angles of the quadrilateral are 67.5°, 90°, 112.5° and 90° respectively.

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Answer 2

Step-by-step explanation:

Given :-

three angles of a quadrilateral are in the ratio 3:4:5 .the difference of the least and the greatest of these angle is 45 degree

To Find :-

find all angles

Solution

let

Angles = 3x, 4x and 5x

Sum of angle = 3x + 4x + 5x = 14x

Fourth angle = (360 - 14x)

Now,

A/q

5x - 3x = 45

2x = 45

x = 45/2

x = 22.5

Hence,

Angles are

3x = 3(22.5) = 67.5⁰

4x = 4(22.5) = 90⁰

360 - 14x = 90⁰

5x = 5(22.5) = 112.5⁰