Math Problem Statement

Find the measure of the indicated angle in the diagram where two parallel lines are cut by a transversal, and one angle is given as 130°.

Solution

The image shows a pair of parallel lines cut by a transversal, with one angle marked as 130°, and the question is asking for the value of the indicated angle (marked with a "?" symbol).

To solve this:

  1. The 130° angle and the "?" angle are supplementary angles because they are on the same side of the transversal and lie between the parallel lines (these are known as consecutive interior angles).

  2. Supplementary angles sum to 180°. Thus, we can find the "?" angle by subtracting 130° from 180°.

?=180130=50? = 180^\circ - 130^\circ = 50^\circ

Thus, the measure of the indicated angle is 50°.

Would you like more details or have any further questions?

Here are 5 relative questions for further practice:

  1. What are alternate interior angles, and how do they relate to parallel lines?
  2. Can two adjacent angles be both supplementary and congruent?
  3. If the given angle was 120°, what would the measure of the indicated angle be?
  4. What is the relationship between corresponding angles when a transversal cuts parallel lines?
  5. How can you prove that two angles are vertical angles?

Tip: Always remember, consecutive interior angles formed by a transversal with parallel lines are supplementary (their sum is 180°).

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Math Problem Analysis

Mathematical Concepts

Geometry
Parallel Lines
Transversals
Supplementary Angles
Consecutive Interior Angles

Formulas

Supplementary Angles Formula: Angle 1 + Angle 2 = 180°

Theorems

Consecutive Interior Angles Theorem: Consecutive interior angles formed by a transversal with parallel lines are supplementary.

Suitable Grade Level

Grades 6-8