Question

the angles of a qudilatral are in the ratio 6:5:4:3 find thier measure​

Answer 1

$\huge{\color{blue}{\boxed{ \color{green}{\underline{\color{red}{\underbrace{\overbrace{\mathfrak{⭐Answer✍}}}}}}}}}$

Given :-

• Angles of quadrilateral in form of ratio.
• Ratio :- 6:5:4:3

To find :-

• All angles

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${ \color{purple}{ \mathtt{As \: \: we \: \: know \: \: that \: \: sum \: \: of}}} \\ {\color{purple}{ \mathtt{ all \: \: angles \: \: of \: \: quadrilateral \: \: is \: \: 180°.}}}$

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Let:-

• Ratio in the form of x .
• Therefore :- 6x , 5x , 4x , 3x

So ,according to the question:-

$\mathtt{ \bold{\leadsto{6x +5x + 4x + 3x=360°}}}$

$\mathtt{\leadsto{ 18x =360°}}$

$\\ \mathtt{ \leadsto{x = \frac{360}{18} }}$

$\color{green} \large \mathtt{ \leadsto{x = 20 \degree}}$

Therefore all angles are ,

$\Large{\boxed{\color{orange}{\mathtt{6x = 6×20= \boxed{120°}}}}}</strong><strong>$

$\Large{\boxed{\color{orange}{\mathtt{5x = 5×20= \boxed{100°}}}}}</strong><strong>$

$\Large{\boxed{\color{orange}{\mathtt{4x = 4×20= \boxed{80°}}}}</strong><strong>}</strong><strong>$

$\Large{\boxed{\color{orange}{\mathtt{3x = 3×20= \boxed{60°}}}}}</strong></p><p><strong>$

Answer 2

Given :-

Ratio of angles of a quadrilateral = 6 : 5 : 4 : 3

To Find :-

The first angle.

The second angle.

The third angle.

The fourth angle.

Analysis :-

Consider the common ratio as a variable.

Make an equation accordingly.

Then find the value of the variable and substitute it in the angles as well.

Solution :-

Consider the common ratio as 'x'. Then the angles would be 6x, 5x, 4x and 3x.

We know that,

Sum of a quadrilateral = 360°

Making an equation,

6x + 5x + 4x + 3x = 360

18x = 360

Finding x,

x = 350/18

x = 20

Finding the angles,

6x = 6 × 20 = 120°

5x = 5 × 20 = 100°

4x = 4 × 20 = 80°

3x = 3 × 20 = 60°

Therefore, the angles are 120°, 100°, 80° and 60° respectively.