Question

Find the value of x if x,(2x+13°),(3x+10°) and ( x- 6°) are all the angles of a quadrilateral?

Answer 1

Answer:

x=49

Step-by-step explanation:

In a quadrilateral,

sum of angles=360⁰

Therefore,

x+2x+13⁰+3x+10⁰+x-6⁰=360⁰

7x+17=360⁰

7x=343

x=49

Answer 2

Given :

• $\tt\:x°~,~(2x+13)°~,~(3x+10)°~and~(x-6)°$ are all the angles of a quadrilateral.

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To find :

• Measure of all the angles = ?

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Concept to be used :

In order to find the measure of all the four angles in the quadrilateral we first need to calculate the value of x.

Now how would we calculate the value of x ?

For calculating the value of x , we would use the angle sum property of a quadrilateral. This property states that :

$\small{\underline{\boxed{\mathrm{Angles~in~a~quadrilateral~=~360°}}}}$

Therefore we would add all the given angles and then equate it with 360° . Doing so we will get the value of x and then we would get the value of all the angels.

Hope am clear let's solve :D~

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Solution :

Following the angle sum property let's add all the given angles and equate it with 360°

$\tt\:x°+(2x+13)°+(3x+10)°+(x-6)°=360°$

Multiplying the signs and removing the brackets

$\tt\implies\:x+2x+13+3x+10+x-6=360°$

Arranging the terms and proceeding with simple calculation

$\tt\implies\:x+2x+3x+x+13+10-6=360°$

$\tt\implies\:3x+3x+x+13+10-6=360°$

$\tt\implies\:6x+x+13+10-6=360°$

$\tt\implies\:7x+13+10-6=360°$

$\tt\implies\:7x+23-6=360°$

$\tt\implies\:7x+17=360°$

Transposing +17 to RHS it becomes -17

$\tt\implies\:7x=(360-17)°$

$\tt\implies\:7x=343°$

Transposing 7 to RHS it goes to the denominator

$\tt\implies\:x=\frac{343°}{7}$

Reducing the fraction to the lower terms

$\tt\implies\:x=\cancel{\frac{343°}{7}}$

$\tt\color{navy}{\implies\:x~=~49°}$

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$\tt\therefore\:The~four~angles~of~the~quadrilateral~are~:$

• x°

⠀⠀ = $\small{\mathfrak{49°}}$

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• ( 2x + 13 )°

⠀⠀ = ( 2 × 49 ) + 13

⠀⠀ = 98 + 13

⠀⠀ = $\small{\mathfrak{111°}}$

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• ( 3x + 10 )°

⠀⠀ = ( 3 × 49 ) + 10

⠀⠀ = 147 + 10

⠀⠀ = $\small{\mathfrak{157°}}$

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• ( x - 6 )°

⠀⠀ = 49 - 6

⠀⠀ = $\small{\mathfrak{43°}}$

So we got the four angles as $\tt\color{purple}{49°~, ~111°~, ~157°~and~43°}$

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Verification :

For any quadrilateral the angles should sum upto 360° .

Henceforth,

$\sf\:49°+111°+157°+43°=360°$

$\sf\leadsto\:160°+157°+43°=360°$

$\sf\leadsto\:317°+43°=360°$

$\sf\leadsto\:360°=360°$

$\sf\leadsto\:LHS=RHS$

Hence Verified !~

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Note :- Scroll left to right to view the answer properly !~

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