Given two parallel lines cut by a transversal, if one of the alternate interior angles measures $m_1=61.8°$, what is the measure of the corresponding alternate interior angle?

• A. $61.8°$
• B. $28.2°$
• C. $118.2°$
• D. $90°$

Answer: (A)

Verified step by step guidance

1. Identify the given information: two parallel lines are cut by a transversal, and one alternate interior angle measures \$61.8^\circ$.
2. Recall the property of alternate interior angles when two parallel lines are cut by a transversal: alternate interior angles are congruent, meaning they have equal measures.
3. Since the given angle is an alternate interior angle, the corresponding alternate interior angle on the opposite side of the transversal will have the same measure.
4. Write the equation expressing this equality: if \(m_1 = 61.8^\circ\), then the corresponding alternate interior angle \(m_2 = m_1 = 61.8^\circ\).
5. Conclude that the measure of the corresponding alternate interior angle is \$61.8^\circ$ based on the congruence property.