As angle 6y° and angle( 13y - 10 )° are interior angles on the same side of transversal their sum will be equal to 180° .
Then :-
[tex]6y + 13y - 10 = 180[/tex]
[tex] 19y - 10 = 180[/tex]
[tex]19y = 180 + 10[/tex]
[tex]19y = 190[/tex]
[tex]y = \frac{190}{19} [/tex]
[tex]y = 10[/tex]
Which means :-
= 13y - 10
= 13 × 10 - 10
= 130 - 10
= 120°
Then angle 6y :-
= 6 × 10
= 60°
As angle 60° and angle 9x + 12° are a linear their sum will also add up to form 180° .
Which can be written as :-
[tex]60 + 9x + 12 = 180[/tex]
[tex]9x + 72 = 180[/tex]
[tex]9x = 180 - 72[/tex]
[tex]9x = 108[/tex]
[tex]x = \frac{108}{9} [/tex]
[tex]x = 12[/tex]
Then :-
= Angle 9x + 12
= 9 × 12 + 12
= 108 + 12
= 120°
Therefore , the value of y = 10 and the value of x = 12 .
