Question

9. The angles of a quadrilateral are in the ratio 1:2:3 : 4. Find all the four angles of the
quadrilateral.
​

Answer 1

Question :-

• The angles of a quadrilateral are in the ratio 1 : 2 : 3 : 4. Find all the four angles of the  Quadrilateral.

Given :-

• Ratio of angles 1 : 2 : 3 : 4

To Find :-

• All four angles of Quadrilateral

Explanation :-

Let the all four angles of a quadrilateral to be 1x, 2x, 3x, and 4x.

As we know, the sum of all interior angle of a quadrilateral is 360°.

According To the Theorem,

$\Longrightarrow{1x+2x+3x+4x=360\textdegree$

$\Longrightarrow{3x+7x=360\textdegree$

$\Longrightarrow{10x=360\textdegree$

$\huge{\Longrightarrow{x=\frac{360}{10} \textdegree}$

$\boxed{\bold{\Longrightarrow{x=36\textdegree}}}$

Now, putting the value of 'x' in all angles

$\Longrightarrow{1(x) = 1(36\textdegree)=\bold{36\textdegree}$

$\Longrightarrow{2(x) = 2(36\textdegree)=\bold{72\textdegree}$

$\Longrightarrow{3(x) = 3(36\textdegree)=\bold{108\textdegree}$

$\Longrightarrow{4(x) = 4(36\textdegree)=\bold{144\textdegree}$

Hence, the value of all angles in quadrilateral are 36°, 72°, 108°, 144°.

@Agamsain❤️

Answer 2

Correct Question : –

The angles of a quadrilateral are in the ratio 1 : 2 :3 : 4. Find all the four angles of the quadrilateral.

Answer : –

The angles are 36° , 72° , 108° and 144°

Step-by-step explanation : –

Let the quadrilateral be ABCD, and let the angles of the quadrilateral be 1x , 2x , 3x and 4x respectively,

Therefore,

$\sf{\implies \: 1x + 2x + 3x + 4x = 360}$

$\sf{\implies \: 10x = \: 360}$

$\sf{ \implies \: x = \: \dfrac{360}{10}}$

$\leadsto \underline{\boxed{ \sf{x =36}}}$

Now, let's find the measure of all angles,

First angle ( 1x )

$\sf{\implies \: 1 \times 36}$

$\leadsto \underline{\boxed{ \sf{1x ={36\degree}}}}$

Second angle ( 2x )

$\sf{\implies \: 2 \times 36}$

$\leadsto \underline{\boxed{ \sf{2x ={72 \degree}}}}$

Third angle ( 3x )

$\sf{\implies \: 3 \times 36}$

$\leadsto \underline{\boxed{ \sf{3x ={108 \degree}}}}$

Fourth angle ( 4x )

$\sf{\implies \: 4 \times 36}$

$\leadsto \underline{\boxed{ \sf{4x ={144 \degree}}}}$

Hence, the angles are 36° , 72° , 108° and 144°

Now, Verification

$\sf{\implies \: 36 + 72 + 108 + 144 = 360}$

$\sf{\implies \: 108 + 252 = 360}$

$\sf{\implies \: 360 = 360}$

L.H.S = R.H.S

$\bf{Hence, \: Verified \: !}$