SSC CGL 2022 PYQ — Question 54

The correct answer is option 2 i.e. 273.

AB = DB and AC = DC

∠DBC = (2x - 4)°

∠ABD = 58°,

∠ACB = (y + 15)° and ∠DCB = 63°

If all three sides of the triangle are equivalent to the corresponding three sides of the other triangle, then both triangles are said to be congruent by the SSS rule.

Since AB = DB and AC = DC and BC is a common side

Therefore, triangles $\triangle ABC \cong \triangle DBC$

So, ∠ABC = ∠ DBC = $\frac 1 2$ × ∠ABD = 58/2 = 29°

According to the given values, (2x - 4)° = 29

⇒ 2x = 33°

Also, angle ACB = angle DCB = 63°

⇒ (y + 15)° = 63°

⇒ y = 48°

Now, 2x + 5y = 33° + 240° = 273°