Question

g > chapter 3 > lesson 3.1.2 > problem 3 - 22 examine the relationships in the diagram at right. then solve for x and y, if possible. justify your work using angle relationships. hint ∠119° and ∠y are supplementary angles, and ∠y and ∠5x + 11° are corresponding angles. more help: see the homework help for problem 2 - 55 in lesson 2.1.5 if you need further help solving for x and y.

Explanation:

Step1: Find the value of y

Since ∠119° and ∠y are supplementary angles, the sum of supplementary angles is 180°. So, 119°+y = 180°. Solving for y:
y=180 - 119
y = 61°

Step2: Find the value of x

Since ∠y and ∠(5x + 11)° are corresponding angles and corresponding angles are equal when lines are parallel, we set them equal to each other.
5x+11=y
Substitute y = 61 into the equation:
5x+11 = 61
Subtract 11 from both sides:
5x=61 - 11
5x = 50
Divide both sides by 5:
x = 10

Answer:

x = 10, y = 61