Question

In figure AB ⊥ AE, BC ⊥ AB, CE = DE and ∠AED = 120°, then find ∠ECD.

Answer 1

Step-by-step explanation:

Given In figure AB ⊥ AE, BC ⊥ AB, CE = DE and ∠AED = 120°, then find ∠ECD.

• Given angle AED = 120 degree.
• AB is perpendicular to AE
• Therefore angle EAB = 90 degree
• BC is perpendicular to AB
• Therefore angle DBA = 90 degree
• From angle sum property of quadrilateral ABDE we get
• Angle EAB + angle AED + angle EDB + angle DBA = 360 degree
• So 90 + 120 + angle EDB + 90 = 360 degree
•   300 + angle EDB = 360
•    Or angle EDB = 360 – 300
•  Or angle EDB = 60 degree
• So angle ECD = 60 degree (since similar angle)
• Also CE = DE  
• From base angle theorem we get
•  Angle EDC = angle ECD = 60 degree

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Answer 2

Answer:

60°

Step-by-step explanation:

Given In figure AB ⊥ AE, BC ⊥ AB, CE = DE and ∠AED = 120°, then find ∠ECD.

Given angle AED = 120 degrees.

AB is perpendicular to AE

Therefore angle EAB = 90 degree

BC is perpendicular to AB

Therefore angle DBA = 90 degree

From angle sum property of quadrilateral ABDE we get

Angle EAB + angle AED + angle EDB + angle DBA = 360°

So 90 + 120 + angle EDB + 90 = 360°

 300° + angle EDB = 360°

  Or angle EDB = 360° – 300°

Or angle EDB = 60°

So angle ECD = 60° (since similar angle)

Also CE = DE  

From base angle theorem we get

Angle EDC = angle ECD = 60°