Question

The angles of a quadrilateral are in ratio 2:5:6:7 . Find the measure of each angle of the quadrilateral. ​

Answer 1

AnswEr:

Angles are 36°, 90°, 108° and 126°

ExplanaTion:

Given that,

• Angles of a quadrilateral are in ratio 2:5:6:7

We have to find the measure of each angle.

Let the angles be, 2x, 5x, 6x and 7x

we know that,

Sum of angles of quadrilateral = 360°

: $\implies$ $\sf{\angle{A} + \angle{B} + \angle{C} + \angle{D} = 360^{\circ}}$

: $\implies$ 2x + 5x + 6x + 7x = 360°

: $\implies$ 20x = 360°

: $\implies$ x = $\sf{\dfrac{360^{\circ}}{20}}$

: $\implies$ $\sf{\purple{x\:=\:18^{\circ}}}$

$\rule{200}2$

Now, put the value of x for find the measure of each angle.

★ $\sf{\angle{A}\:=\:2x}$

: $\implies$ $\sf{\angle{A}\:=\:2 \times 18}$

: $\implies$ $\sf{\angle{A}\:=\:36^{\circ}}$

★ $\sf{\angle{B}\:=\:5x}$

: $\implies$ $\sf{\angle{B}\:=\:5 \times 18}$

: $\implies$ $\sf{\angle{B}\:=\:90^{\circ}}$

★ $\sf{\angle{C}\:=\:6x}$

: $\implies$ $\sf{\angle{C}\:=\:6 \times 18}$

: $\implies$ $\sf{\angle{C}\:=\:108^{\circ}}$

★ $\sf{\angle{D}\:=\:7x}$

: $\implies$ $\sf{\angle{D}\:=\:7 \times 18}$

: $\implies$ $\sf{\angle{D}\:=\:126^{\circ}}$

Hence, angles are 36°, 90°, 108° and 126°

Answer 2

$\huge{\red{\underline {\underline {Question :-}}}}$

⭐ The angles of a quadrilateral are in ratio 2:5:6:7 . Find the measure of each angle of the quadrilateral?

$\huge{\purple{\boxed {\boxed {Answer :-}}}}$

☑ The measure of each angle of the quadrilateral are 36,90,108,&126.

$\huge{\green{\underline {\underline {Solution :-}}}}$

Given Ratio of angles :- 2:5:6:7

Let each angle of the quadrilateral be,

Sum of all the angles of a quadrilateral =360°

=> 2x + 5x + 6x + 7x = 360°

=> 20x = 360°

$= > x \: = \frac{360}{20}$

=> x = 18°

So, the required angles are

2x = 2× 18 = 36

5x = 5 × 18 = 90

6x = 6 × 18 = 108

7x = 7 × 18 = 126

∴ The measure of each angle of the quadrilateral are 36,90,108,&126.

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