Math Problem Statement

What is the measure of angle 13 given that the measure of angle 1 is 85°?

Solution

We are given that lines lml \parallel m and lines cdc \parallel d, along with the measure of angle 1 being 85°. We are asked to find the measure of angle 13.

To solve this, let's proceed step by step:

Step 1: Use Corresponding Angles

Since lml \parallel m, angle 1 is corresponding to angle 5. Thus, angle 5 must also be 85° (because corresponding angles are congruent).

5=85°\angle 5 = 85°

Step 2: Use Vertical Angles

Next, notice that angle 5 and angle 13 are vertical angles. Vertical angles are always congruent, so:

13=5=85°\angle 13 = \angle 5 = 85°

Conclusion:

The measure of angle 13 is 85°.

Would you like further details or explanations on this? Here are some related questions that can deepen your understanding:

  1. How are corresponding angles determined in parallel lines?
  2. Why are vertical angles always congruent?
  3. Can you explain alternate interior angles in parallel lines?
  4. What would be the measure of angle 7?
  5. What are the relationships between other pairs of angles in this diagram?

Tip: When dealing with parallel lines and a transversal, corresponding and alternate angles often provide key relationships for solving problems.

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Math Problem Analysis

Mathematical Concepts

Parallel Lines
Transversals
Corresponding Angles
Vertical Angles

Formulas

Corresponding Angles Theorem: If two parallel lines are cut by a transversal, then each pair of corresponding angles are equal.
Vertical Angles Theorem: When two lines intersect, opposite (vertical) angles are equal.

Theorems

Corresponding Angles Theorem
Vertical Angles Theorem

Suitable Grade Level

Grades 8-10