Given:
Given that the angles (12y + 5)° and (18y - 7)° are vertical angles.
Also, given the other angle is (3x + 1)°
We need to determine the value of x.
Value of y:
Since, the angles (12y + 5)° and (18y - 7)° are vertical angles, then they must be congruent.
Thus, we have;
[tex]12y+5=18y-7[/tex]
[tex]-6y+5=-7[/tex]
[tex]-6y=-12[/tex]
[tex]y=2[/tex]
Thus, the value of y is 2.
Value of x:
From the figure, it is obvious that the angles (18y - 7)° and (3x + 1)° are linear pairs.
Thus, we have;
[tex]18y-7+3x+1=180[/tex]
Substituting y = 2, we get;
[tex]36-7+3x+1=180[/tex]
[tex]3x+30=180[/tex]
[tex]3x=150[/tex]
[tex]x=50[/tex]
Thus, the value of x is 50.
