the figure point D is an interior point of equilateral triangle ABC. It is given that DA = DB. Point E is also given so that ∠DBE = ∠DBC and BE = AB. Find ∠E.
Answers
Given : point D is an interior point of equilateral triangle ABC. DA = DB. Point E is so that ∠DBE = ∠DBC and BE = AB.
To Find : ∠E
Solution:
Join CD
Compare ΔBDE & ΔBDC
BD = BD ( Common)
∠DBE = ∠DBC ( given )
BE = BC (∵ BE = AC & AB = BC = AC - equilateral triangle)
=> ΔBDE ≅ ΔBDC
=> DE = CD
=> ∠E = ∠BCD
Compare ΔADC & ΔBDC
DA = DB ( given )
DC = DC ( common)
AC = BC ( Sides of equilateral triinagle)
=> ΔADC ≅ ΔBDC
=> ∠ACD = ∠BCD
∠ACD +∠BCD = ∠A = 60°
=> ∠ACD = ∠BCD = 30°
∠E = ∠BCD = 30°
∠E. = 30°
Learn More:
In the given figure AD is internal bisector of angle A and CE is ...
https://brainly.in/question/11611726
O is a point in the interior of a square ABCD such that OAB is an ...
https://brainly.in/question/600221
suppose ABC is an isosceles triangle with AB=AC;BD and CE are ...
https://brainly.in/question/1939503
Answer:
E=30
Step-by-step explanation:
please mark me as BRAINLIEST ans
