Question

In a triangle abc with side ab=ac and angle bac=20 degree ,d is a point on side acand bc=ad. Find angle dbc

Answer 1

AB=AC  

It means given triangle is Isosceles triangle.

So,

∠ACB= ∠ABC

Also given that,

∠BAC = 20°

<BAC + ∠ACB + ∠ABC = 180°

∠ACB + ∠ABC  = 180 - 20 = 160

∡ACB = ∡ABC=80∘ (Using angle sum property)

Let E be a point inside the triangle such that EB=EC=BC.

Since ∡ABE=(180°−20°)/2 − 60° =  20°,

we can see that △ABD and △BAE are congruent.

Hence,

∡DBC = ∡ABC − ∡ABD = ∡ABC − ∡BAE

⇒80°−10°=70°

∡DBC  = 70°

Answer 2

Step-by-step explanation:

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