Question

The anglees of a quadrilateral are in the ratio 4:5:3,the difference between greatest angle and least angle is 42degree.Find all angles​

Answer 1

Given :-

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

Difference between greatest angle and the least angle = 42°

To Find :-

The value of all angles of the quadrilateral.

Analysis :-

Consider the common ratio as x and let the angles be 4x, 5x and 3x respectively.

According to the question, make an equation by showing it's difference.

Solve x and substitute them to get the angles.

Subtract the angles we got from the total angle of a quadrilateral to get the 4th one.

Solution :-

Let us consider the common ratio to be x

Then the angles would be 4x, 5x and 3x respectively.

Given that,

The difference between greatest angle and least angle is 42°

According to the question,

$\sf 5x-3x=42$

$\sf 2x=42$

$\sf x=\dfrac{42}{2}$

$\sf x=21$

Hence, the value of x is 21

Then, the angles of the quadrilaterals would be

$\sf 4x=4 \times 21=84^{o}$

$\sf 5x=5 \times 21=105^{o}$

$\sf 3x= 3 \times 21=63^{o}$

Sum of the angles = 84 + 105 + 63 = 252°

Finding the fourth angle,

Fourth angle = $\sf 360-252=108^{o}$

Therefore, the angles are 84°, 105°, 63° and 108° respectively.

Answer 2

REFER TO THE ATTACHMENT

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