Question 1:
For this case we have that by definition, if a and b are two parallel lines, then the corresponding angles are congruent, that is, we can write 3x + 2 and x + 8 as supplementary angles:
[tex](3x + 2) + (x + 8) = 180\\3x + 2 + x + 8 = 180\\4x + 10 = 180\\4x = 180-10\\4x = 170\\x = \frac {170} {4}\\x = 42.5[/tex]
We look for the value of the angles:
[tex]3 (42.5) + 2 = 129.5\ degrees\\42.5 + 8 = 50.5 \ degrees[/tex]
ANswer:
[tex]x = 42.5\\3 (42.5) + 2 = 129.5\ degrees\\42.5 + 8 = 50.5 \ degrees[/tex]
Question 2:
For this case we have that by definition, the equation of a line of the slope-intersection form is given by:
[tex]y = mx + b[/tex]
Where:
m: It's the slope
b: It is the cutoff point with the y axis
Now, in the equation [tex]y = 2x + 3[/tex]
[tex]m = 2\\b = 3[/tex]
By definition, if two lines are parallel, their slopes are equal. Also, if two lines are perpendicular, then the product of their slopes is -1.
So:
The slope of a line parallel to the given line is:
[tex]m = 3[/tex]
The slope of a line perpendicular to the given line is:
[tex]3 * m = -1\\m = - \frac {1} {3}[/tex]
ANswer:
[tex]3\\- \frac {1} {3}[/tex]
