To answer this question we will set and solve equations.
1) Notice that the angles that measure 2x+18 degrees and 3x-7 degrees are vertical angles. Since the lines with the marks are parallel, then:
[tex]2x+18^{\circ}=3x-7^{\circ}.[/tex]Adding 7degrees-2x to the above result we get:
[tex]\begin{gathered} 2x+18^{\circ}+7^{\circ}-2x=3x-7^{\circ}+7^{\circ}-2x, \\ 25^{\circ}=x. \end{gathered}[/tex]2) Notice that the angles that measure 78 degrees and y+10 degrees are corresponding angles. Since the lines with the marks are parallel, then:
[tex]78^{\circ}=y+10^{\circ}.[/tex]Subtracting 10 degrees from the above result we get:
[tex]\begin{gathered} 78^{\circ}-10^{\circ}=y+10^{\circ}-10^{\circ}, \\ 68^{\circ}=y. \end{gathered}[/tex]3) Recall that the interior angles of a triangle add up to 180 degrees, therefore:
[tex]y+10^{\circ}+3x-7^{\circ}+d=180^{\circ}.[/tex]Substituting the above result we get:
[tex]68^{\circ}+10^{\circ}+3(25^{\circ})-7^{\circ}+d=180^{\circ}.[/tex]Simplifying the above result we get:
[tex]146^{\circ}+d=180^{\circ}.[/tex]Therefore:
[tex]d=34^{\circ}.[/tex]Answer:
[tex]\begin{gathered} x=25^{\circ},\text{ vertical angles.} \\ y=68^{\circ},\text{ corresponding angles.} \\ d=34^{\circ},\text{ interior angles of a triangle add up to }180^{\circ}. \end{gathered}[/tex]