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Sagot :
[tex] \star \blue{ \frak{To \: find :}}[/tex]
[tex] \\ \\ [/tex]
- value of x
[tex] \\ \\ [/tex]
[tex] \star \blue{ \frak{solution:}}[/tex]
[tex] \\ \\ [/tex]
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]
[tex] \\ \\ [/tex]
Step by step expansion:
[tex] \\ \\ [/tex]
[tex] \dashrightarrow \sf(10x - 20) \degree + (6x + 8)\degree = 180 \degree \\[/tex]
[tex] \\ \\ [/tex]
[tex] \dashrightarrow \sf10x - 20 \degree + 6x + 8\degree = 180 \degree \\[/tex]
[tex] \\ \\ [/tex]
[tex] \dashrightarrow \sf10x +6x- 20 \degree + 8\degree = 180 \degree \\[/tex]
[tex] \\ \\ [/tex]
[tex] \dashrightarrow \sf16x- 20 \degree + 8\degree = 180 \degree \\[/tex]
[tex] \\ \\ [/tex]
[tex] \dashrightarrow \sf16x- 12\degree = 180 \degree \\[/tex]
[tex] \\ \\ [/tex]
[tex] \dashrightarrow \sf16x = 180 \degree + 12\degree\\[/tex]
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[tex] \dashrightarrow \sf16x =192\degree\\[/tex]
[tex] \\ \\ [/tex]
[tex] \dashrightarrow \sf \: x = \frac{192\degree}{16\degree} \\[/tex]
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[tex] \dashrightarrow \sf \: x = 12 \degree[/tex]
[tex] \\ \\ [/tex]
[tex]\therefore \underline {\textsf{\textbf{Value of x is \red{12\degree}}}}[/tex]
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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