Math Problem Statement

ABCD is a parallelogram. Find ∠CFG. Given that ∠AEB = 65° and ∠CFE = 18°.

Solution

In the given parallelogram ABCDABCD, we are tasked with finding CFG\angle CFG.

Steps to Solve:

  1. Identify the angles in the diagram:

    • AEB=65\angle AEB = 65^\circ
    • CFE=18\angle CFE = 18^\circ
    • ABCDABCD is a parallelogram, which implies opposite sides are parallel, and the corresponding angles are equal.
  2. Using angle relationships:

    • Since ABCDABCD is a parallelogram, ABDCAB \parallel DC and EFEF is a transversal. Therefore, EAB\angle EAB (or AEB\angle AEB) is supplementary to CFG\angle CFG, because they are on the same side of the transversal EFEF.
    • Supplementary angles sum to 180180^\circ, so: CFG=180AEB=18065=115\angle CFG = 180^\circ - \angle AEB = 180^\circ - 65^\circ = 115^\circ

Thus, CFG=115\angle CFG = 115^\circ.

Would you like more details or have any further questions?

Related questions:

  1. What are the properties of a parallelogram in terms of angles and sides?
  2. How do transversal lines affect angles in parallel line systems?
  3. Can you explain the concept of supplementary angles?
  4. What is the relationship between alternate interior angles in parallelograms?
  5. How do you calculate unknown angles using given angles and geometric properties?

Tip: In a parallelogram, opposite angles are always equal, and adjacent angles are supplementary (add up to 180180^\circ).

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Math Problem Analysis

Mathematical Concepts

Geometry
Angles in Parallelograms
Transversals

Formulas

Supplementary Angles: ∠A + ∠B = 180°

Theorems

Properties of Parallelograms
Supplementary Angles Theorem

Suitable Grade Level

Grades 8-10