Question

Please show work so I can learn thanks

Answer 1

Explanation:

when the two angles are added they are equal to 180 degree. (corresponding angles property)

x+8+3X+2=180

4X+10=180

4X=170

X=44.25 DEGREES

Answer 2

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:

`(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`

We look for the value of the angles:

`3 (42.5) + 2 = 129.5\ degrees\\42.5 + 8 = 50.5 \ degrees`

ANswer:

`x = 42.5\\3 (42.5) + 2 = 129.5\ degrees\\42.5 + 8 = 50.5 \ degrees`

Question 2:

For this case we have that by definition, the equation of a line of the slope-intersection form is given by:

`y = mx + b`

Where:

m: It's the slope

b: It is the cutoff point with the y axis

Now, in the equation
`y = 2x + 3`

`m = 2\\b = 3`

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:

`m = 3`

The slope of a line perpendicular to the given line is:

`3 * m = -1\\m = - \frac {1} {3}`

ANswer:

`3\\- \frac {1} {3}`