Find x, then find the measurement of both angles.

A: x = 20; both angles measure 112 degrees
B: x = 20; both angles measure 110 degrees
C: x = 30; both angles measure 114 degrees
D: x = 30; both angles measure 118 degrees.

C:x=30:both angles measure 114 degrees

Step-by-step explanation:

in 2 parallel lines with a transversal, the marked angles are alternate exterior angles, which means that both angles are congruent(equal)

ur equation is: 2x+54=4x-6

60=2x

x=30

we have now eliminated options a and b

CHECK:

2*30+54=60+54=114

4*30-6=120-6=114

114=114

c is the correct answer

step-by-step explanation:

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3