Question

based on the diagram below, which statement is true?

1. ( a parallel b )
2. ( a parallel c )
3. ( b parallel c )
4. ( d parallel e )

Explanation:

Step1: Check parallel line conditions

For two lines to be parallel, the corresponding angles or alternate - interior angles formed by a transversal should be equal.

• For \(a\) and \(b\):

The angles formed by the transversal with \(a\) and \(b\) are \(110^{\circ}\) and \(60^{\circ}\) (not equal). So \(a
parallel b\).

• For \(a\) and \(c\):

The angles formed by the transversal with \(a\) and \(c\) are \(110^{\circ}\) and \(115^{\circ}\) (not equal). So \(a
parallel c\).

• For \(b\) and \(c\):

The angles formed by the transversal with \(b\) and \(c\) are \(60^{\circ}\) and \(115^{\circ}\) (not equal). So \(b
parallel c\).

• For \(d\) and \(e\):

The sum of the adjacent angles formed by the transversal with \(d\) and \(e\) (one is \(60^{\circ}\) and the other is \(120^{\circ}\), \(60 + 120=180^{\circ}\)). When the sum of consecutive - interior angles is \(180^{\circ}\), the two lines are parallel.

Answer:

1. \(d\parallel e\)