Math Problem Statement

Transversal c intersects the parallel lines, a and b, in the picture below.

image d5c9df0b83ee4a54a613c74200b2000e

What is the value of x? A. 102

B. 96

C. 84

D. 78

Solution

To solve for the value of xx, let's consider the following steps, assuming the image provides the necessary angle relationships.

Key Points:

  1. Parallel Lines and Transversal: When a transversal crosses parallel lines, angles are either congruent (equal) or supplementary (add up to 180180^\circ) based on their positions.
  2. Alternate Interior Angles: These are equal.
  3. Corresponding Angles: These are equal.
  4. Supplementary Angles: If two angles are on the same side of the transversal, they are supplementary.

Analyzing the Problem:

From the provided options and based on the typical configuration:

  1. Identify the relationship of xx with other angles.
  2. Solve for xx using the relationships (e.g., x+other angle=180x + \text{other angle} = 180^\circ for supplementary angles or x=other anglex = \text{other angle} for congruent angles).

Without the image specifics, the exact calculation cannot be determined. However, if the angle corresponding to xx is given (or supplementary to a known angle), you can deduce xx by:

  • Setting x=180other anglex = 180^\circ - \text{other angle} (for supplementary).
  • Or, x=other anglex = \text{other angle} (for congruence).

Likely Result:

If x=84x = 84^\circ based on the supplementary or congruent relationships, then the answer is: C. 84

If you want me to clarify further or check the exact angles from the image, let me know!

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Math Problem Analysis

Mathematical Concepts

Geometry
Angles
Parallel Lines
Transversal

Formulas

Sum of supplementary angles = 180°
Congruent angles

Theorems

Alternate Interior Angles Theorem
Corresponding Angles Postulate
Supplementary Angles Theorem

Suitable Grade Level

Grades 7-9