Lines a and b are parallel. line c  is a transversal. find the measures of all angles formed by a, b,  and c, if: one of the angles has measure of 150°.

150º and 30º angles.

Step-by-step explanation:

When you have parallel lines that are vut by a transversal line, you get a 2 pairs of 4 angles, this pairs are congruent or suplementary, this means that the sum of their angles is 180º or they are equal. So ig you have that one angle is 150º the other one since is suplementary must be 30º, since 150*30=180, and all of the angles are equal to these two, 150º and 30º angles.

x = -3

y = -18

step-by-step explanation:

to solve by substitution, substitute one variable and solve for the other. then substitute again to find the remaining variable.

x-1/3(3x-9) = -3 since y=3x-9 substittute y.

x-1/3(3x-9)=-3

x + x +3 = -3

2x+3=-3

2x+3-3= -3-3

2x=-6

x=-3

substitute again into y=3x-9

y=3(-3)-9

y=-9-9

y=-18

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4