Question

1. given x and y.

a. x = 15, y = 45
b. x = 20, y = 60
c. x = 18, y = 72
d. x = 21, y = 83
(1) select the pair of lines in the diagram below that must be parallel if ∠6 ≅ ∠8. if there are two lines that must be parallel, select
one.\
a. k and j
b. d and c
c. a and i
d. q and j
e. none

Explanation:

Step1: Analyze vertical angles and linear pairs

The sum of angles around a point is \(360^{\circ}\). Here, we have three angles of \(3x^{\circ}\) and one angle of \(y^{\circ}\). So, \(3x + 3x+3x + y=360\), which simplifies to \(9x + y=360\).

Step2: Solve for \(x\) and \(y\)

We can check each option:

• Option A: If \(x = 15,y = 45\), then \(9\times15+45=135 + 45=180

eq360\).

• Option B: If \(x = 20,y = 60\), then \(9\times20+60=180+60 = 240

eq360\).

• Option C: If \(x = 18,y = 72\), then \(9\times18+72=162+72=234

eq360\).

• Option D: If \(x = 21,y = 81\), then \(9\times21+81=189+81=270

eq360\).

Answer:

E. None