Question

The three anates of
tourage
The angles of a quadrilateral are in the ratio 3: 5:7:9. Find the measure of each
these angle

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Answer 1

Given :

• Angles of a Quadrilateral are in the ratio 3:5:7:9.

To Find :

• Measure of each angle of Quadrilateral.

Solution :

Let Angles of Quadrilateral be 3x , 5x , 7x , 9x.

As we know that Sum of all the angles of a Quadrilateral is 360° . So ,

$\longmapsto\tt{3x+5x+7x+9x=360\degree}$

$\longmapsto\tt{24x=360\degree}$

$\longmapsto\tt{x=\cancel\dfrac{360}{24}}$

$\longmapsto\tt{x=15}$

Value of x is 15...

Therefore :

$\longmapsto\tt{Measure\:of\:1st\:Angle=3(15)}$

$\longmapsto\tt\bf{45\degree}$

$\longmapsto\tt{Measure\:of\:2nd\:Angle=5(15)}$

$\longmapsto\tt\bf{75\degree}$

$\longmapsto\tt{Measure\:of\:3rd\:Angle=7(15)}$

$\longmapsto\tt\bf{105\degree}$

$\longmapsto\tt{Measure\:of\:4th\:Angle=9(15)}$

$\longmapsto\tt\bf{135\degree}$

Answer 2

AnsWer :

• Angles are 45° , 75° , 105° and 135° .

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Given :

• Ratio of angles of a quadrilateral i.e. 3:5:7:9 .

To Find :

• Measure of each angle

Solution :

☯ Angle Sum property of a quadrilateral states that sum of all interior angles of the quadrilateral is equal to sum total of 360° .

• Let the unknown angle be x .

Now , Angles are 3x , 5x , 7x and 9x .

$: \implies \small \sf 3x\:+\:5x\:+\:7x\:+\:9x\:=\:360°$

$: \implies \small \sf 24x\:=\:360°$

$: \implies \small \sf x\:=\: \dfrac{360°}{24}$

$\implies \large \sf {\orange{x\:=\:15°}}$

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Now , measure of angles are equal to :

• Angle 1 = 3(15) = 45°

• Angle 2 = 5(15) = 75°

• Angle 3 = 7(15) = 105°

• Angle 4 = 9(15) = 135°

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