The adjoining figure is a rectangle whose diagonals AC and BD intersect at O. If ∠OAB = 27°, then find ∠OBC.

In a rectangle, the diagonals are equal in length and bisect each other. This means that they cut each other in half at the point of intersection, which is point O in this case.

Since the diagonals bisect each other, this means that ∠OAB = ∠OBA. Given that ∠OAB = 27°, this means that ∠OBA is also 27°.

In a rectangle, the sum of the angles is 180°. Therefore, ∠OBC = 180° - ∠OBA = 180° - 27° = 153°.

So, ∠OBC = 153°.

Sure, here is the step by step solution:

Step 1: In a rectangle, the diagonals are equal and bisect each other. Therefore, triangle OAB is congruent to triangle ODC.

Step 2: Since the triangles are congruent, their corresponding angles are equal. Therefore, ∠OAB = ∠ODC = 27°.

Step 3: In a rectangle, each angle is a right angle (90°). Therefore, ∠ABC = 90°.

Step 4: ∠OBC is part of ∠ABC. Therefore, ∠OBC = ∠ABC - ∠OAB = 90° - 27° = 63°.

So, ∠OBC = 63°.