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What is the value of x?



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What Is The Value Of X Enter Your Answer In The Box X class=

Sagot :

WindyMint

[tex] \star \blue{ \frak{To \: find :}}[/tex]

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  • value of x

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[tex] \star \blue{ \frak{solution:}}[/tex]

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So to find value of x , we have to apply Linear Pair.

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Equation formed:

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[tex] \bigstar \boxed{ \tt(10x - 20) \degree + (6x + 8)\degree = 180 \degree} \\ [/tex]

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Step by step expansion:

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[tex] \dashrightarrow \sf(10x - 20) \degree + (6x + 8)\degree = 180 \degree \\[/tex]

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[tex] \dashrightarrow \sf10x - 20 \degree + 6x + 8\degree = 180 \degree \\[/tex]

[tex] \\ \\ [/tex]

[tex] \dashrightarrow \sf10x +6x- 20 \degree + 8\degree = 180 \degree \\[/tex]

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[tex] \dashrightarrow \sf16x- 20 \degree + 8\degree = 180 \degree \\[/tex]

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[tex] \dashrightarrow \sf16x- 12\degree = 180 \degree \\[/tex]

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[tex] \dashrightarrow \sf16x = 180 \degree + 12\degree\\[/tex]

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[tex] \dashrightarrow \sf16x =192\degree\\[/tex]

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[tex] \dashrightarrow \sf \: x = \frac{192\degree}{16\degree} \\[/tex]

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[tex] \dashrightarrow \sf \: x = 12 \degree[/tex]

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[tex]\therefore \underline {\textsf{\textbf{Value of x is \red{12\degree}}}}[/tex]

SalmonWorldTopper

Step-by-step explanation:

Linear Pairs of Angles: If a ray stands on a line, then the two adjacent angles so formed is 180° or sum of the angles forming a linear pair is 180°.

Now, from figure:

Given angles are on the straight line

They are linear pair

(10x - 20)° + (6x + 8)° = 180°

Open all the brackets on LHS.

⇛10x - 20° + 6x + 8° = 180°

⇛10x° + 6x - 20 + 8° = 180°

Add and subtract the variables and Constants on LHS.

⇛16x - 12° = 180°

Shift the number -12 from LHS to RHS, changing it's sign.

⇛16x = 180° + 12°

Add the numbers on RHS.

⇛16x = 192°

Shift the number 16 from LHS to RHS, changing it's sign.

⇛x = 192°/16

Simplify the fraction on RHS to get the final value of x.

⇛x = {(192÷2)/(16÷2)}

= (96/8)

= {(96÷2)/(8÷2)}

= (48/4)

= {(48÷2)/(4÷2)}

= (24/2)

= {(24÷2)/(2÷2)} = 12/1

Therefore, x = 12

Answer: Hence, the value of x is 12.

Explore More:

Now,

Finding each angle by substitute the value of x.

Angle (10x-20)° = (10*12-20)° = (120-10)° = (100)° = 100°

Angle (6x+8)° = (6*12+8)° = (72 + 8)° = (80)° = 80°

Verification:

Check whether the value of x is true or false. By substituting the value of x in equation.

(10x-20)° + (6x + 8)° = 180°

⇛(10*12-20)° + (6*12 + 8)° = 180°

⇛(120 - 20)° + (72 + 8)° = 180°

⇛(100)° + (80)° = 180°

⇛100° + 80° = 180°

⇛180° = 180°

LHS = RHS, is true for x = 12.

Hence, verified.

Please let me know if you have any other questions.

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