Question

three angles are in the ratio 4ratio 5 ratio 3 ratio. the difference of the least and the greatest of these angle is 42 degree. find all the four angle of the quadrilateral​

Answer 1

Question:-

• Three angles are in the ratio 4ratio 5 ratio 3 ratio. the difference of the least and the greatest of these angle is 42 degree.

Find:-

• Find all the four angle of the quadrilateral

Solution:

⇒Let the constant ratio be 'x'

Then, let the three angles are 4x,3x,5x

⇒Let the greatest angle of quadrilateral

= 5x and smallest angle = 3x

⇒As it is Given , difference between the greatest and the smallest angle = 42°

⇒5x - 3x = 42°

⇒2x = 42

⇒x = 21

So, the three angles of quadrilateral are:-

⇒4x = 4 × 21 = 84°

⇒3x = 3 × 21 = 63°

⇒5x = 5 × 21 = 105°

We know that ,

Sum of all the four anlges of quadrilateral = 360°

Let the fourth angle be' Y '

84° + 63° + 105° + Y = 360°

252°+ Y = 360°

Y = 360° - 252° = 108°

Hence,

All the four angles of quadrilateral are

84° , 63° , 105° , 108°.

_______________________________

Answer 2

☞Correct Question:

Three angles are in the ratio 4ratio 5 ratio 3 ratio. The difference of the least and the greatest of these angle is 42 degree. Find all the four angle of the quadrilateral.

☞Required Answer:

The four angles of the quadrilateral are

63°, 84°, 105°, 108°.

☞Solution:

☞Given:

=>Three angles are in the ratio 4 ratio 5 ratio 3 ratio.

=> Difference between the least and greatest angle = 42°

☞To find:

Four angles of the quadrilateral.

☞How to solve

=> Three angles are in ratio 4 ratio, 5 ratio, 3 ratio.

=> Let the three angles of quadrilateral are 4x, 5x and 3x.

=> Greatest angle = 5x

=> Least angle = 3x

=> It is given that difference of the least and greatest angle = 42°

=> So, our equation becomes

5x - 3x = 42°

2x = 42°

x = 21°

Therefore, value of x = 21°

Verification:

✩Put x = 21 in equation 5x - 3x = 42

5×21 - 3×21 = 42

105 - 63 = 42

42 = 42

LHS = RHS

✩Hence verified

=> Three angles of quadrilateral are 3x, 4x, 5x

✩Value of x = 21°

First angle = 3x = 3×21 = 63°

Second angle = 4x = 4×21 = 84°

Third angle = 5x = 5×21 = 105°

Fouth angle = ?

=> Sum of four angles of quadrilateral = 360°

✩Let the fourth angle be 'A'

63° + 84° + 105° + A = 360°

252° + A = 360°

A = 360° - 252°

A = 108°

☞Therefore, four angles of a quadrilateral are 63°, 84°, 105°, 108°.

Verification

✩Sum of four angles of quadrilateral = 360°

63° + 84° + 105° + 108° = 360°

360° = 360°

LHS = RHS

Hence verified