In the figure, d, e, and f are parallel lines. What is the value of x? Enter your answer in the box.

The value of x is 130°.

Solution:

The reference image for the solution is attached below.

Let A, B and C be the given angles.

m∠A = 70° and m∠C = (x – 20)°

If two lines are parallel then their corresponding angles are congruent.

Line e and line f are parallel lines and ∠B and ∠C are corresponding angles.

m∠B = m∠C

m∠B = (x – 20)°

Angle A and angle B are in the same line. So, they form a linear pair.

m∠A + m∠B = 180°

70° + x – 20° = 180°

50° + x = 180°

Subtract 50°  on both sides of the equation.

x = 180° – 50°

x = 130°

The value of x is 130°.

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