Question

if the angles of quadrilateral are In the ratio 4:6:8:2 find each other of quadrilateral ​

Answer 1

Given :-

• If the angles of quadrilateral are in the ratio 4:6:8:2 .

To Find :-

• The each angle of quadrilateral .

Solution :-

We know, that sum of all angles of a quadilateral is 360°. (Angle sum property of a quadilateral)

First angle of quadilateral is 4x°.

The Second angle of quadilateral is 6x°

The Third angle of quadilateral 8x°

The fourth angle of quadilateral 2x°

4x° + 6x° + 8x° + 2x° = 360°

➝ 10x° + 10x° = 360

➝ 20x° = 360°

➝ x = $\cancel{\dfrac{360}{20}}$

➝ x = 18

• First angle of quadilateral is 4x° = 4 × 18 = 72°

• The Second angle of quadilateral is 6x° = 6 × 18 = 108°.

• The Third angle of quadilateral 8x° = 8 × 18 = 144°

• The fourth angle of quadilateral 2x° = 2 × 18 = 36°

Let's Verify :-

4x° + 6x° + 8x° + 2x° = 360°

➝ 72 + 108 + 144 + 36 = 360

➝ 360° = 360°

Hence, verified ✔

_____________________________________

$\setlength{\unitlength}{1 cm}\begin{picture}(0,0)\thicklines\qbezier(1,1)(1,1)(6,1)\put(0.4,0.5){\bf D}\qbezier(1,1)(1,1)(1.6,4)\put(6.2,0.5){\bf C}\qbezier(1.6,4)(1.6,4)(6.6,4)\put(1,4){\bf A}\qbezier(6,1)(6,1)(6.6,4)\put(6.9,3.8){\bf B}\end{picture}$

Answer 2

$\huge\bf\underline\pink{Given:-}$

The angles of quadrilateral are in ratio is

4:6:8:2

$\huge\bf\underline\purple{To find:-}$

Angles of quadrilateral

$\huge\bf\underline\pink{Concept used}$

The sum of all angles in quadrilateral is 360°

$\huge\bf\underline\purple{Solution:-}$

Let the angles are 4x,6x,8x,2x(4:6:8:2)

So,We know that sum of angles is 360°

So,

4x+6x+8x+2x=360°

20x=360°

x=18°

Now 4x = 4(18) = 72°

6x = 6 (18) = 108°

8x= 8(18) = 144°

2x=2(18)= 36°

$\huge\bf\underline\pink{Conclusion:-}$

The angles in quadrilateral are 72°,108°,144°,36°

Hope u understood clearly