Math Problem Statement

Find EDC

Find EDC

Solution

To find the measure of angle EDC\angle EDC, we analyze the geometry of the given circle and the angles involved. Let’s proceed step by step:


Given:

  1. E,A,B,C,DE, A, B, C, D are points on the circumference of a circle.
  2. EAC=72\angle EAC = 72^\circ.
  3. AEB=25\angle AEB = 25^\circ.

Step 1: Use the Inscribed Angle Theorem

  • The inscribed angle EAC\angle EAC subtends the same arc as EDC\angle EDC (both subtend arc ECEC).
  • By the Inscribed Angle Theorem, EAC=EDC\angle EAC = \angle EDC.

Step 2: Conclude

Since EAC=72\angle EAC = 72^\circ, we have:

EDC=72\angle EDC = 72^\circ

Thus, EDC=72\angle EDC = 72^\circ.


Would you like a detailed explanation of how the Inscribed Angle Theorem works or help with related problems?


5 Related Questions:

  1. How is the Inscribed Angle Theorem applied in cyclic quadrilaterals?
  2. Can the measure of other angles in this diagram be determined?
  3. How can BCD\angle BCD be calculated from this configuration?
  4. What is the relationship between central angles and inscribed angles?
  5. Can the arcs in this circle be used to solve additional angle problems?

Tip:

In cyclic quadrilaterals, opposite angles are supplementary. Always check if this property can simplify your calculations.

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Math Problem Analysis

Mathematical Concepts

Circle Geometry
Inscribed Angles
Cyclic Quadrilaterals

Formulas

Inscribed Angle = Half the Measure of the Intercepted Arc

Theorems

Inscribed Angle Theorem

Suitable Grade Level

Grades 9-11