The anglees of a quadrilateral are in the ratio 4:5:3,the difference b

1.	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» 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 $\sf 4x=4 \times 21=<klux>84</klux>^{o}$ $\sf 5x=5 \times 21=<klux>105</klux>^{o}$ $\sf 3x= 3 \times 21=63^{o}$ 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.

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»

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

$\sf 4x=4 \times 21=<klux>84</klux>^{o}$

$\sf 5x=5 \times 21=<klux>105</klux>^{o}$

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

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.