Question

1. if ( r parallel s ), which of the following must be true?

a. ( b = 140 ^ { circ } )
b. ( d = 140 ^ { circ } )
c. ( a = 40 ^ { circ } )
d. ( c = 40 ^ { circ } )

Explanation:

Step1: Find the value of \(a\)

Since \(a\) and the \(40^{\circ}\) angle are supplementary (they form a linear - pair), \(a + 40^{\circ}=180^{\circ}\), so \(a = 140^{\circ}\).

Step2: Use the property of parallel lines and transversal

Because \(r\parallel s\), \(d=a\) (corresponding angles). So \(d = 140^{\circ}\).

Step3: Analyze other angles

\(b\) and \(a\) are vertical angles, so \(b=a = 140^{\circ}\). \(c\) and \(d\) are supplementary (\(c + d=180^{\circ}\)), so \(c=40^{\circ}\). But we need to check which one must be true.
Since \(r\parallel s\), by the property of parallel lines and transversal (corresponding angles), \(d\) (which is equal to \(a\) (vertical angles) and \(a\) is supplementary to \(40^{\circ}\)) \(d = 140^{\circ}\)

Answer:

B. \(d = 140^{\circ}\)