Proofs About Angles Practice

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Two parallel, inclined lines labeled as m and n are separated by a distance. A diagonal line labeled as t intersects m and n at a bottom left to top right incline.

In the diagram, given m∥n
, m∠5=117°
. Investigate the patterns of angles created when parallel lines are cut by a transversal to identify m∠2
.

(1 point)
m∠2=
°


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Answer 1

To find \( m∠2 \) given that \( m∠5 = 117° \) and that lines \( m \) and \( n \) are parallel (denoted as \( m∥n \)), we can use the properties of angles formed when parallel lines are intersected by a transversal.

In this case, angle \( 5 \) and angle \( 2 \) are alternate interior angles. When two parallel lines are cut by a transversal, alternate interior angles are equal. Therefore, we can say:

\[ m∠2 = m∠5 \]

Since \( m∠5 = 117° \), we have:

\[ m∠2 = 117° \]

Thus, the answer is:

\[ m∠2 = 117° \]