SSC CGL 2021 PYQ — Question 57

The correct answer is option 2 i.e. 28°

Given :

∠ABC = 34° and CD = BD

Calculations :

∠ACB = 90°

In  $\Delta ACB$

⇒ ∠ABC + ∠ACB + ∠ BAC = 180

⇒ 34 + 90 + ∠ BAC = 180

⇒ ∠BAC = 180 - 124

⇒ ∠BAC = 56

We know ABDC is a cyclic quadrilateral

The sum of opposite angle is 180

⇒ ∠ A + ∠ D = 180

⇒ 56 + ∠ D = 180

⇒ ∠ D = 124

CD and BD are equals such that angles opposite to these sides are also equal

In $\Delta BDC$, we know

⇒ CD = BD and ∠ DBC = ∠ BCD

⇒ ∠ DBC + ∠ BCD + ∠BDC = 180

⇒ 2 ∠ DBC = 180 - 124

⇒ 2 ∠ DBC = 56

⇒ ∠ DBC = 28