Question

The angles of a quadrilateral are in the ratio 2 : 3 : 4 : 6. Find the measure of each of the

four angles.​

Answer 1

$\bold{\underline{\underline{\huge{\sf{AnsWer:}}}}}$

First angle = 48°

Second angle = 72°

Third angle = 96°

Fourth angle = 144°

$\bold{\underline{\underline{\large{\sf{StEp\:by\:stEp\:explanation:}}}}}$

GiVeN :

• Angles of a quadrilateral are in ratio 2:3:4:6

To FiNd :

• Measure of each of the four angles.

SoLuTioN :

Let x be the common multiple of the ratio of the angles.

$\tt{\therefore{Four\:angles\:are:}}$

1. 2x
2. 3x
3. 4x
4. 6x

Property :

$\sf{Sum\:of\:all\:the\:angles\:of\:a\:quadrilateral\:is\:360\:\degree}$

Using this property, we will solve for x and then plug in the value of x to find the measure of the angels.

$\hookrightarrow$ $\tt{2x\:+\:3x\:+\:4x\:+\:6x\:=\:360}$

$\hookrightarrow$ $\tt{5x\:+\:10x=360}$

$\hookrightarrow$ $\tt{15x\:=\:360}$

$\hookrightarrow$ $\tt{x\:=\:{\dfrac{360}{15}}}$

$\hookrightarrow$ $\tt{x=24}$

Now, block in the calculated value of x in the ratio of the angles.

$\tt{\therefore{Four\:angles\:of\:quadrilateral\:are:}}$

1. $\tt{2x\:=\:2\:\times\:24\:=\:48\:\degree}$
2. $\tt{3x\:=\:3\:\times\:24\:=\:72\:\degree}$
3. $\tt{4x\:=\:4\:\times\:24\:=\:96\:\degree}$
4. $\tt{6x\:=\:6\:\times\:24\:=\:144\:\degree}$

$\bold{\underline{\huge{\sf{VeRiFiCaTiOn:}}}}$

We can verify such question via property used to solve the it.

Here, we used the property of :

Sum of all the angles of a quadrilateral is 360°

So, if we add up all the angles derived after solving for x it should be equal to 360°

Let's check.

$\hookrightarrow$ $\tt{2x+3x+4x+6x=360}$

$\hookrightarrow$ $\tt{48+72+96+144=360}$

$\hookrightarrow$ $\tt{120+240=360}$

$\hookrightarrow$$\tt{360=360}$

LHS = RHS

Answer 2

Question : The angles of a quadrilateral are in the ratio 2 : 3 : 4 : 6. Find the measure of each of the four angles.

Solution :

Sum of all angles of quadrilateral = 360°

Given :

Angles of quadrilateral are in the ratio 2:3:4:6.

To find :

The measures of four angles = ?

Let the measures of four angles of the quadrilateral be (2x)°, (3x)°, (4x)° and (6x)°.

Atq,

$\: \: \: \: \: \: 2x + 3x + 4x + 6x = 360 \\ = > 15x = 360 \\ = > x = \frac{360}{15} \\ = > x = 24$

Hence, measures of four angles are : (2×24)° = 48°

(3×24)° = 72°

(4×24)° = 96°

(6×24)° = 144°.

To check that our calculated angles are correct :

Verification :

$\:\:\:\:2x+3x+4x+6x = 360$

$= >48+72+96+144 =360$

$=> 360=360$

$LHS=RHS$