Question

Three angles of aquadrilateral are in the ratio 4:3:5. the difference between the greatest and the smallest Angle is 42 degree . find all the for angle of the quadrilateral

Answer 1

Ratio of the three angles of a quadrilateral = 4 : 3 : 5

let the constant ratio be 'x'

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

let the greatest angle of quadrilateral
= 5x and smallest angle = 3x

Given , difference between the greatest and the smallest angle = 42°

5x - 3x = 42°

2x = 42

x = 21

so now the three angles of quadrilateral are

4x = 4 × 21 = 84°

3x = 3 × 21 = 63°

5x = 5 × 21 = 105°

since , we know that

sum of all the four anlges of quadrilateral = 360°

let the fourth angle be' A '

84° + 63° + 105° + A = 360°

252°+ A = 360°

A = 360° - 252° = 108°

therefore,
all the four angles of quadrilateral are

84° , 63° , 105° , 108°.
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Answer 2

Answer:

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