SSC CGL 2024 PYQ — Question 58

The correct answer is Option 3 i.e. 100°.

Let ∠AOB = α and ∠COD = β

Since O is an interior point such that OA = OC, this means O lies on the line segment that connects the midpoints of the diagonals.

Since the diagonals bisect each other and intersect at right angles

⇒ ∠AOB + ∠BOC + ∠COD + ∠DOA = 360^∘

Since OA = OC, triangles OAC and OAB will be isosceles o,

⇒ ∠AOB = ∠COD

Let ∠AOB = α and ∠COD = α

The remaining angles ∠BOC and ∠DOA will also equal β

Since O lies within the rhombus, we know that the sum of the angles around point O must equal 360^∘

⇒ α + β + α + β = 360^∘

Thus, 

⇒ 2α + 2β = 360

⇒ α + β = 180

Now,

⇒ ∠DOB = ∠AOB + ∠BOC = α + β = 180

Now,

⇒ 5/9th of ∠DOB

⇒ 5/9 × 180

⇒ 5 × 20 = 100°

Therefore, five-ninths of the degree measure of ∠DOB is 100°