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.
