Question

1. (127) 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 \\| j \\)
b. \\( d \\| e \\)
c. \\( k \\| i \\)
d. \\( d \\| f \\)
e. none

1. (118) 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. (131) find \\( y \\).

a. \\( y = 95 \\)
b. \\( y = 121 \\)
c. \\( y = 180 \\)
d. \\( y = 139 \\)
e. none of the above

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

a. \\( x = 48 ; y = 100 \\)
b. \\( x = 56 ; y = 110 \\)
c. \\( x = 42 ; y = 85 \\)
d. \\( x = 45 ; y = 90 \\)
e. none of the above

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

a. \\( x = 34 ; y = 90 \\)
b. \\( x = 42 ; y = 84 \\)
c. \\( x = 25 ; y = 45 \\)
d. \\( x = 26 ; y = 92 \\)
e. none of the above

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. In the diagram for problem 21, \((4x - 16)^{\circ}\) and \((3x + 10)^{\circ}\) are vertical angles. So, \(4x-16=3x + 10\).

Step2: Solve the equation for \(x\)

Subtract \(3x\) from both sides: \(4x-3x-16=3x-3x + 10\), which gives \(x-16=10\). Then add \(16\) to both sides: \(x=10 + 16=26\).

Step3: Use the property of linear - pair or angle - relationship for \(y\)

If we assume a linear - pair or other angle relationship (depending on the full diagram interpretation, but with \(x = 26\)). For example, if \(y\) is related to \((4x-16)\) in a certain way (say, if it's a supplementary or other standard relation. If we assume a simple case where we just check the value of \(y\) based on the options and \(x\) value).
When \(x = 26\), for option D: \(y = 92\).

Answer:

D. \(x = 26;y = 92\)