Question

In a triangle ABC with side AB=AC and angle BAC=20°, D is a point on side AC and BC=AD. Find angle DBC ?a) 50b) 65c) 45d) 70Please provide complete solution....

Answer 1

Answer:

∡DBC  = 70°       Option D

Explanation:

Given that,

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°