Question

Parallel lines r and s are intersected by a transversal line m.
Label a pair of corresponding angle measures (6x +11) and (3y+8)°.
The angle labeled (3y + 8)° is a linear pair with an angle measure of (10x - 13)°.
Set up algebra equations and solve for x and y.

Answer 1

Answer: x= 8   y= 17

Step-by-step explanation: 6*8 = 48+11=59

3*17=51+8=59

Answer 2

Answer:

x = 11.375

y = 23.75

Step-by-step explanation:

Corresponding angles:  A pair of angles that are in the same relative position at each point where a straight line intersects two other straight lines.

If the two lines are parallel, the corresponding angles are equal. 

Therefore:

⇒ (6x + 11)° = (3y + 8)°

⇒ 6x + 11 = 3y + 8

⇒ 6x + 3 = 3y

⇒ 3y = 6x + 3

Angles on a line sum to 180°.  

Therefore:

⇒ (3y + 8)° + (10x - 13)° = 180°

⇒ 3y + 8 + 10x - 13 = 180

⇒ 3y + 10x = 185

⇒ 3y = 185 - 10x

Substitute the first equation into the second equation and solve for x:

⇒ 6x + 3 = 185 - 10x

⇒ 16x = 182

⇒ 16x = 182

⇒ x = 11.375

Substitute the found value of x into one of the equations and solve for y:

⇒ 3y = 6(11.375) + 3

⇒ 3y = 68.25 + 3

⇒ 3y = 71.25

⇒ y = 23.75