Question

1. (l27) select the pair of lines in the diagram below that must be parallel if \\( \angle 6 \cong \angle 8 \\). if there are no lines that must be parallel, select

one.\
a. \\( k \parallel j \\)
b. \\( d \parallel e \\)
c. \\( k \parallel i \\)
d. \\( d \parallel f \\)
e. none

1. (l18) find \\( x \\) and \\( y \\).

a. \\( x = 15 ; y = 45 \\)
b. \\( x = 20 ; y = 60 \\)
c. \\( x = 18 ; y = 72 \\)
d. \\( x = 21 ; y = 85 \\)
e. none of the above

1. (l31) find \\( y \\).

Explanation:

Step1: Use the angle - sum property of a full circle

The sum of angles around a point is \(360^{\circ}\). So, \(3x + 3x+3x + y=360\).

Step2: Simplify the equation

\(9x + y=360\). Also, note that \(y = 3x\) (vertically opposite angles).

Step3: Substitute \(y = 3x\) into the equation

Substitute \(y = 3x\) into \(9x + y=360\). We get \(9x+3x = 360\).

Step4: Solve for \(x\)

\(12x=360\), then \(x=\frac{360}{12}=30\).

Step5: Solve for \(y\)

Since \(y = 3x\), then \(y=3\times30 = 90\).

Answer:

\(y = 90\)