Question

given that ( p parallel q ) and ( r parallel s ), name all angles supplemental to ( angle 16 ).
a. ( angle 2, angle 5, angle 6, angle 9, angle 10, angle 13, angle 14, angle 19 )
b. ( angle 3, angle 7, angle 8, angle 11, angle 12, angle 17 )
c. ( angle 6, angle 9, angle 10, angle 13 )
d. ( angle 7, angle 8, angle 11, angle 12, angle 15, angle 16, angle 17, angle 18 )

Explanation:

Step1: Recall the definition of supplementary angles

Supplementary angles are two angles whose sum is \(180^{\circ}\).

Step2: Identify angles that form a linear - pair with \(\angle16\)

• \(\angle15\) and \(\angle16\) form a linear - pair (sum to \(180^{\circ}\)), \(\angle17\) and \(\angle16\) form a linear - pair (sum to \(180^{\circ}\)).

Step3: Use the properties of parallel lines (\(r\parallel s\) and \(p\parallel q\))

• Since \(r\parallel s\) and using the property of corresponding angles and consecutive interior angles:
• \(\angle16\) and \(\angle8\) are consecutive interior angles (supplementary as \(r\parallel s\)), \(\angle16\) and \(\angle11\) are consecutive interior angles (supplementary as \(p\parallel q\)).
• \(\angle16\) and \(\angle7\) (because \(\angle7=\angle8\) (vertical angles) and \(\angle8 + \angle16=180^{\circ}\)), \(\angle16\) and \(\angle12\) (because \(\angle12=\angle11\) (vertical angles) and \(\angle11+\angle16 = 180^{\circ}\)).

Answer:

B. \(\angle3,\angle7,\angle8,\angle11,\angle12,\angle17\)