Question

angles 1, 2, and 3 combine to form a straight line, so m∠1 + m∠2 + m∠3 = 180°. since lines f and g are parallel, m∠1 = m∠5 and m∠3 = m∠6 by the alternate interior angles theorem. therefore, m∠5 + m∠2 + m∠6 = 180° by substitution.
angles 1, 2, and 3 combine to form a straight line, so m∠1 + m∠2 + m∠3 = 180°. since lines f and g are parallel, m∠1 = m∠5 and m∠3 = m∠6 by the alternate interior angles theorem. therefore, m∠5 + m∠2 + m∠6 = 180° by subtraction.
angles 1, 2, and 3 combine to form a straight line, so m∠1 + m∠2 + m∠3 = 180°. since lines f and g are parallel, m∠1 = m∠5 and m∠3 = m∠6 by the same - side interior angles theorem. therefore, m∠5 + m∠2 + m∠6 = 180° by substitution.
angles 1, 2, and 3 combine to form a straight line, so m∠1 + m∠2 + m∠3 = 180°. since lines f and g are parallel, m∠1 = m∠5 and m∠3 = m∠6 by the corresponding angles theorem. therefore, m∠5 + m∠2 + m∠6 = 180° by substitution.
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Explanation:

Step1: Recall angle - line relationship

Angles on a straight - line sum to 180°. So, \(m\angle1 + m\angle2 + m\angle3=180^{\circ}\).

Step2: Use parallel - line angle theorem

Since \(f\parallel g\), by the Alternate Interior Angles Theorem, \(m\angle1 = m\angle5\) and \(m\angle3 = m\angle6\).

Step3: Substitute equal angles

Substitute \(m\angle1\) with \(m\angle5\) and \(m\angle3\) with \(m\angle6\) in the equation \(m\angle1 + m\angle2 + m\angle3 = 180^{\circ}\), we get \(m\angle5 + m\angle2 + m\angle6 = 180^{\circ}\).

Answer:

The first two statements (where the Alternate Interior Angles Theorem is used for substitution) are correct. The third statement is incorrect as it uses the Same - Side Interior Angles Theorem wrongly. The fourth statement is incorrect as it uses the Corresponding Angles Theorem wrongly. The correct reasoning is that angles 1, 2, and 3 combine to form a straight line (\(m\angle1 + m\angle2 + m\angle3 = 180^{\circ}\)), and since lines \(f\) and \(g\) are parallel, \(m\angle1 = m\angle5\) and \(m\angle3 = m\angle6\) by the Alternate Interior Angles Theorem, so \(m\angle5 + m\angle2 + m\angle6 = 180^{\circ}\) by substitution.