Ask a New Question
Menu

Proofs About Angles Practice

Complete this assessment to review what you’ve learned. It will not count toward your grade.
1 of 51 of 5 Items
Question
Use the image to answer the question.

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=
°

3 answers

In the scenario described, when two parallel lines (m and n) are intersected by a transversal (t), various angles are formed that have specific relationships to one another due to the properties of parallel lines.

Given that m∠5 = 117°, we can identify the position of angle 5 with respect to the transversal and the parallel lines. Angle 5 is likely an exterior angle formed on one side of the transversal.

Angles formed by parallel lines and a transversal follow these rules:

  1. Corresponding angles are equal.
  2. Alternate interior angles are equal.
  3. Consecutive interior angles are supplementary (add up to 180°).
  4. Alternate exterior angles are equal.

Since angle 5 is an exterior angle, we need to find where angle 2 is located relative to angle 5.

  • If angle 5 is an exterior angle above the line m, then angle 2 would be a corresponding angle below line n. Hence, m∠2 will equal m∠5. Thus: m∠2 = 117°.

Conclusion: m∠2 = 117°.

117 is not the answer

Apologies for the confusion. Let's analyze the angle relationships again based on the given information.

Given that \( m \parallel n \) and \( m\angle 5 = 117° \), we need to determine \( m\angle 2 \) based on the properties of angles formed when a transversal intersects parallel lines.

  1. Since \( m \) and \( n \) are parallel and \( t \) is the transversal, we know that:
    • \( m\angle 5 \) (an exterior angle) and \( m\angle 2 \) (an interior angle) are alternate interior angles.
    • Alternate interior angles are equal.

However, if angle 5 is outside of the parallel lines and angle 2 is an interior angle formed between the parallel lines, then they are supplementary. Therefore:

\[ m\angle 5 + m\angle 2 = 180° \]

Substituting the value we know:

\[ 117° + m\angle 2 = 180° \]

Now, we can solve for \( m\angle 2 \):

\[ m\angle 2 = 180° - 117° \]

Calculating this gives:

\[ m\angle 2 = 63° \]

Thus, the correct answer is:

m∠2 = 63°.