Math Problem Statement

Other than itself, which angle is congruent to ∠ECF?

Solution

To determine which angle is congruent to ECF\angle ECF in the provided diagram, let's examine the structure of the angles and lines.

Solution

  1. Identify ECF\angle ECF: ECF\angle ECF is the angle formed at point CC, between line segments ECEC and CFCF.

  2. Check for Vertical Angles: Since the lines intersect at point CC, vertical angles are formed. Vertical angles are congruent. Therefore, the angle directly opposite ECF\angle ECF would also be congruent to it.

  3. Identify the Congruent Angle: The angle opposite ECF\angle ECF across point CC is DCH\angle DCH.

Thus, the angle congruent to ECF\angle ECF (other than itself) is: DCH\angle DCH

Would you like more details on why vertical angles are congruent or have further questions?


Related Questions:

  1. What are vertical angles, and why are they always congruent?
  2. How can you identify congruent angles in intersecting lines?
  3. Are there other pairs of congruent angles in this diagram?
  4. What is the difference between adjacent and vertical angles?
  5. How would you calculate the measure of these angles if given additional information?

Tip:

When two lines intersect, vertical (opposite) angles are always congruent. This is a fundamental property in geometry and can be useful in various angle calculations.

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Math Problem Analysis

Mathematical Concepts

Geometry
Congruent Angles
Vertical Angles

Formulas

-

Theorems

Vertical Angle Theorem

Suitable Grade Level

Grade 7