50 points. 1. provide reasons for the proof. given: line p is parallel to line r. prove: ∠1 is supplementary to ∠7.

Given: Line p is parallel to line r.

Alternate exterior angles states that two angles in the exterior of the parallel lines, and on opposite sides of the transversal.

Alternate exterior angles are non-adjacent and congruent.

               [ Alternate exterior angles]

Since, Angles are congruent if they have the same angle measure in degrees

 ....[1]         [by definition of congruent Angles]

Linear pair states that a pair of adjacent angles formed when two lines intersect.

therefore, by definition   and forms a linear pair.

Since, linear pair are always supplementary.

is supplementary to

Supplementary angles states that two angles are supplementary that means they add up to measure 180 degree.

Substitute the equation [1] in above equation we get;

then, by the definition of supplementary angle ;

is supplementary to

fa tha first one you gonna add y to both sides

it look like this

x-y+y=6+y

x=y+6

therefore your answer is

x =y+6

fa tha second one

you gonna flip tha equation

it gonna look like x-4y=y

then add 4 to both sides

it gonna look like tha

x-4 +4 =y +4

so therefore tha answer is x=y+4

step-by-step explanation:

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be