Explanation:
Vertically Opposite Angles: The two intersecting lines with a common point so formed angles Vertically opposite angles and they are equal.
Given: (3x+ 50)° and (6x - 10)°
Asked: find the value of x = ?
Solution:
Angle (3x+ 50)° = Angle (6x - 10)°
Remove to brackets both sides on LHS and RHS.
⇛3x + 50° = 6x - 10°
Shift variables on LHS and Constants on RHS, changing it's sign.
⇛3x - 6x = -10° - 50°
Subtract the and add the values on LHS and RHS.
⇛-3x = -60°
Shift the number 3 from LHS to RHS.
⇛x = -60/-3
Simplify the fraction on RHS to get the final value of x.
⇛x = {(60÷3)/(3÷3)}
⇛x = 20°/1°
Therefore, x = 20°
Answer: Hence, the value of x is 20°
Explore More:
Now, finding the the measure of each angles by putting the value of "x" in their places.
•Angle (3x+ 50)° = (3*20 + 50)° = (60 + 50)° = (100)° = 110.
Next
Angle (6x - 10)° = (6*20 -10)° = (120 - 10)° = (110)° = 110.
Verification:
Check whether the value of x is true or false.
Angle (3x+ 50)° = Angle (6x - 10)°
Substitute the value of x in equation then
⇛Angle (3*20 + 50)° = Angle (6*20 - 10)°
⇛Angle (60 + 50)° = Angel (112 - 10)°
⇛Angle (110)° = Angle (110)°
Angle 110° = Angle 110°
LHS = RHS is true for x = 20°
Hence, verified.