Math Problem Statement

Given that the two lines are parallel and m<7=57, what is the m<1?

Solution

If the two lines are parallel and you are given that m7=57m\angle 7 = 57^\circ, we can find m1m\angle 1 using the properties of parallel lines and their angles.

In the context of parallel lines cut by a transversal, angles 1 and 7 are corresponding angles, meaning they are congruent (equal in measure). Therefore:

m1=m7=57m\angle 1 = m\angle 7 = 57^\circ

Thus, m1=57m\angle 1 = 57^\circ.

Would you like further clarification or more details?

Here are 5 related questions you might want to explore:

  1. What are alternate interior angles, and how do they relate to parallel lines?
  2. How do we find the measure of an angle when two lines are perpendicular?
  3. What is the sum of the interior angles of a triangle?
  4. How can we calculate the exterior angle of a triangle using parallel lines?
  5. What other angle relationships exist when two parallel lines are cut by a transversal?

Tip: Remember that corresponding angles are always equal when two parallel lines are intersected by a transversal!

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Math Problem Analysis

Mathematical Concepts

Geometry
Parallel Lines
Transversal
Angle Relationships

Formulas

Corresponding angles are congruent when two parallel lines are intersected by a transversal

Theorems

Corresponding Angles Postulate

Suitable Grade Level

Grades 7-9