Question

In triangle ADE, angle ADE=140 dgerees and the points B,c lie on sides AD,AE respectively and points A,B,C,D,E are distinct. If lengths AB,BC,CD and DE are all equal, then the measure of triangle EAD is

Answer 1

∠EAD = 10°

Step-by-step explanation:

Let say ∠EAD = x

=> ∠CAB = x  as B lies on AD  & C lies on EA

AB = BC

=> ∠ACB = ∠CAB = x

∠CBD =  ∠ACB +  ∠CAB

=> ∠CBD =  2x

  ∠CDB = 2x  as BC = CD

=> ∠BCD = 180° - 2x - 2x

=> ∠BCD = 180° - 4x

∠ACB + ∠BCD + ∠DCE = 180°  ( straight line)

=> x + 180° - 4x + ∠DCE = 180°

=> ∠DCE = 3x

∠DEC = ∠DCE = 3x  ( as  CD = DE)

Now x + 140° + 3x = 180°

=> 4x = 40°

=> x = 10°

∠EAD = 10°

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Answer 2

Answer:

Angle BCD = 140

Step-by-step explanation: