Question

in the figure shown, ( tparallel x ) and ( kparallel w ) and ( mangle3 = 20^{circ} ). choose the list which includes all of the other angles that measure ( 20^{circ} ).
a 1
b 1,5,7
c 1,14,16
d 1,5,7,9,11,14,16

Explanation:

Step1: Identify vertical angles

Vertical angles are equal. Since \(\angle3 = 20^{\circ}\), \(\angle1=\angle3 = 20^{\circ}\) (vertical angles).

Step2: Use parallel - line properties (corresponding angles)

Because \(k\parallel w\) and \(l\) is a transversal, \(\angle5=\angle1 = 20^{\circ}\) (corresponding angles). Also, \(\angle9=\angle5 = 20^{\circ}\) (corresponding angles as \(t\parallel x\) and \(w\) is a transversal).

Step3: Use parallel - line properties (alternate interior angles)

Since \(k\parallel w\) and \(t\) is a transversal, \(\angle7=\angle3 = 20^{\circ}\) (alternate interior angles). And \(\angle11=\angle7 = 20^{\circ}\) (corresponding angles as \(t\parallel x\) and \(w\) is a transversal).

Step4: Use parallel - line properties (alternate exterior angles)

Because \(k\parallel w\) and \(t\) is a transversal, \(\angle15=\angle3 = 20^{\circ}\) (alternate exterior angles).

Answer:

A. \(1,5,7,9,11,15\)