Question

b. The angles of a quadrilateral are x°, 5x°, 4x* and 2x. Find the value of x​

Answer 1

Answer: x=30

Step-by-step explanation:

Sum of all angles of a quadrilateral = 360°

sum of all angles given = 12x

x= 360/12

x=30

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Answer 2

Clarification:

Here, we are provided that the angles of a quadrilateral are x°, 5x°, 4x° and 2x°.Now, we have to find the value of x°. So, we'll make a suitable equation in order to find the value of x. Thinking, which equation?! As we know that the sum of the angles of a quadrilateral is equivalent to 360°. So, our equation will be :

• Sum of the angles of a quadrilateral = 360°

Then, we'll find the value of x by solving this equation using transposing the terms.

Given:

• The angles of a quadrilateral are x°, 5x°, 4x* and 2x.

To calculate:

• Value of x.

Calculation:

As we know that,

» » Sum of the angles of quadrilateral = 360°

Substituting values,

$\sf {\longrightarrow {x}^{\circ} + {5x}^{\circ} + {4x}^{\circ} + {2x}^{\circ} = {360}^{\circ} }$

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Performing addition of like terms in left hand side (LHS).

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$\sf {\longrightarrow {12x}^{\circ} = {360}^{\circ} }$

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Transposing 12 from LHS to RHS. So, as it is in the multiplication form, its sign will be changed in division form.

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$\sf {\longrightarrow {x}^{\circ} =\cancel{ \dfrac{ {360}^{\circ}}{12} } }$

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$\longrightarrow \underline{\boxed{\sf{ {x}^{\circ} = {30}^{\circ} }}} \: \red{\bigstar}$

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Henceforth,

• Value of x° is 30°.

Verification:

$\underline{ \underline{\rm{LHS }}}$

→ $\rm { Sum \: of \: angles \: of \: quadrilateral}$

→ $\rm { {x}^{\circ} + {5x}^{\circ} + {4x}^{\circ} + {2x}^{\circ} }$

→ $\rm { \red{{30}^{\circ} }+ {5\red{(30)}}^{\circ} + {4\red{(30)}}^{\circ} + {2\red{(30)}}^{\circ} }$

→ $\rm { {30}^{\circ} + {150}^{\circ} + {120}^{\circ} + {60}^{\circ} }$

$\longrightarrow \underline{\boxed{\sf{ {360}^{\circ} }}} \: \red{\bigstar}$ [LHS]

$\underline{ \underline{\rm{RHS }}}$

→ 360°

⠀⠀⠀⠀⠀⠀$\underline{ \underline{\rm{\therefore RHS = LHS }}}$

Hence, verified!