∠1 = ∠4 ( vertically opposite angles )
Then :-
[tex]3x + 10 = 4x - 15[/tex]
[tex]10 = 4x - 15 - 3x[/tex]
[tex]10 = 1x - 15[/tex]
[tex]1x - 15 = 10[/tex]
[tex]1x = 10 + 15[/tex]
[tex]1x = 25[/tex]
Which means :-
∠1 =
= 3x + 10
= 3 × 25 + 10
= 75 + 10
= 85°
∠4 =
= 4x - 15
= 4 × 25 - 15
= 100 - 15
= 85°
Then :-
∠7 = ∠6
∠6 + ∠4 = 180° ( interior angles on the same side of transversal )
∠6 + 85 = 180°
∠6 = 180 - 85
∠6 = 95°
As ;
∠6 = ∠7
∠7 = 95°
Therefore , angle 7 = 95° .
