Question

Use the given information to write an equation and solve the problem. (28-31 in the picture)

Answer 1

Answers :
28/ 120 degrees
29/ 30 degrees
30/ 56 & 124 degrees
31/ 72, 108, 18 degrees

Answer 2

Answer:

28. 120 degrees

29. 30 degrees

30. 56 degrees & 124 degrees

31. 72 degrees, 108 degrees, and 18 degrees

Step-by-step explanation:

We assign variable x for the answer we are looking for (28-29).

28.

Supplement means x + y = 180 degrees. We also know x = 2y. Substitution gives us 3y = 180 degrees, so y = 60 degrees and x = 120 degrees.

29.

Complement means x + y = 90 degrees. We are given 2x = y. Substitution brings us 3x = 90 degrees, x = 30 degrees.

30.

Supplement means x + y = 180 degrees. We are told that y = 2x + 12, so we substitute. This gives 3x + 12 = 180 degrees, x = 56 degrees. Substituting that back into the equation for y, we get 124 degrees.

31.

Supplement means x + y = 180 degrees. Complement means x + z = 90 degrees.  Using our given info, we know y = 6z. We can substitute that in to get x + 6z = 180. Subtracting our second and third equations, we get 5z = 90, z = 18 degrees.  Therefore, x = 72 degrees, y = 108 degrees.