Question

1. in the figure below, line j is parallel to line k and line r is parallel to s. which statement is false?

( a ^ { circ } + d ^ { circ } = 180 ^ { circ } )
( a ^ { circ } = c ^ { circ } )
( b ^ { circ } + e ^ { circ } = 180 ^ { circ } )

Explanation:

Step1: Check \(b^{\circ}+e^{\circ}=180^{\circ}\)

Since \(b^{\circ}\) and \(e^{\circ}\) are adjacent angles forming a linear pair, \(b + e=180^{\circ}\) (by the definition of a linear pair).

Step2: Check \(a^{\circ}=c^{\circ}\)

\(a^{\circ}\) and \(c^{\circ}\) are vertical angles. Vertical angles are equal, so \(a = c\).

Step3: Check \(a^{\circ}+d^{\circ}=180^{\circ}\)

Since \(j\parallel k\) and \(r\parallel s\), \(a^{\circ}\) and \(d^{\circ}\) are not supplementary. There is no property (like same - side interior angles) that would make \(a + d=180^{\circ}\) in this configuration.

Answer:

\(a^{\circ}+d^{\circ}=180^{\circ}\)