SSC CHSL 2024 PYQ — Question 51

The correct answer is option 1 i.e. 30°.

Let us join points BD

Hence, the 2 sides of the ΔBCD i.e. BC and CD are equal

Hence, the ∠CBA and ∠CDB are equal 

Let us denote these 2 angles by x

Now since the sum of the interior angles of the ΔBCD is 180

⇒ 126 + x + x = 180

⇒ x = 27

Now in ΔABD

∠A = $\frac{1}{2}$ ∠BCD

⇒ ∠A = 63

Now the sum of  the interior angles of the ΔABC is 180

⇒ 63 + (27 + 33) + (∠ABC + 27) = 180

⇒ ∠ABC = 30°