Question

6. In adjacent figure check whether AABC = ADCB. If
ZDBC = 45° then find ZACB. Also find ZABC if
BAC = 60°​

Answer 1

Step-by-step explanation:

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Answer 2

Given : figure is a quadrilateral ABCD

            AB = DC ; BD = AC ; ∠BAC = 60° ; ∠DBC = 45°

Since in Δ ABC & Δ DCB

AB = DC

BD = AC

BC = BC

∴ Δ ABC ≅ Δ DCB  (by SSS Axiom of congruency)

Let the point of intersection of the diagonals be point 'O'

In the figure it is given that OB = OC

Since it is an isosceles triangle with sides OB = OC angle opposite to these sides must be equal

⇒ ∠OBC = ∠OCB  = 45°

so in ΔOBC ∠BOC = 180° - 45° - 45°

⇒ ∠BOC = 90°

We now from the figure ∠BOC is the exterior angle for ΔAOB

⇒ ∠BOC = ∠OAB  + ∠OBA

⇒ 90° = 60° + ∠OBA  

⇒ ∠OBA = 30°

So, ∠ABC = ∠ABO + ∠OBC

⇒ ∠ABC = 30° + 45°

   ∴ ∠ABC = 75°