Question

1. given: m∠3 = m∠8 prove: m∠3 + m∠6 = 180° statements reasons

Explanation:

Step1: Substitute given angle - equality

Since \(m\angle3 = m\angle8\) (given), substitute \(m\angle8\) for \(m\angle3\) in the equation \(m\angle3 + m\angle6=180^{\circ}\). We get \(m\angle8 + m\angle6 = 180^{\circ}\).

Step2: Recall same - side interior angles postulate

If two lines are cut by a transversal and the sum of a pair of same - side interior angles is \(180^{\circ}\), then the two lines are parallel. Here, \(\angle8\) and \(\angle6\) are same - side interior angles formed by lines \(j\) and \(k\) and a transversal. So, \(j\parallel k\).

Answer:

Statements:

1. \(m\angle3 = m\angle8\) (Given)
2. \(m\angle3 + m\angle6=180^{\circ}\) (Given)
3. \(m\angle8 + m\angle6 = 180^{\circ}\) (Substitution Property of Equality)
4. \(j\parallel k\) (Same - side Interior Angles Postulate)

Reasons:

1. Given
2. Given
3. Substitution Property of Equality
4. Same - side Interior Angles Postulate