Question

In triangle ABC, ∠DAE = 40°, AD=BD, and AE=EC. Find ∠BAC

Answer 1

∠BAC = 110°  In triangle ABC, ∠DAE = 40°, AD=BD, and AE=EC

Step-by-step explanation:

AD = BD

=> ∠DAB  =  ∠DBA

∠ADE = ∠DAB  +  ∠DBA

=> ∠ADE  = 2∠DAB

AE = EC

=> ∠EAC  =  ∠ECA

∠AED = ∠EAC +  ∠ECA

=> ∠AED = 2 ∠EAC

∠ADE + ∠AED + 40° = 180°

=> 2∠DAB  + 2 ∠EAC = 140°

=> ∠DAB  + ∠EAC = 70°

∠BAC = ∠DAB + 40° +  ∠EAC

=> ∠BAC = ∠DAB  + ∠EAC + 40°

=> ∠BAC = 70° + 40°

=> ∠BAC = 110°

Learn more:

sum of the five exterior angles is 760.remaining 2 angles are equal ...

https://brainly.in/question/12811377

In figure 3.8, ∠ACD is an exterior angle of ΔABC. ∠B =40°,∠A=70 ...

https://brainly.in/question/4557874

If x,y and z are exterior angles of triangle ABC, then find th value of x ...

https://brainly.in/question/7928507