Question

ABCD is a rectangle whose diagonals AC and BD intersect each other at O. If LOAB=28°, find LOBC

Answer 1

heya...

here is you answer...

Answer 2

SOLUTION

We have, ABCD as the given rectangle in which AC & BD are the diagonals that intersect at O.

We know that diagonals of rectangle bisect each other, so

OD= OB = BD/2.........(1) &

OA =OC= AC/2..........(2)

Now in rectangle diagonals are equal, so

AC= BD

From (1) & (2), we get

=) 2OD = 2OA

=) OD= OA

In ∆OAB,

OA= OB

=) ∠OAB= ∠OBA (Angles opposite to equal sides are equal)

=) ∠OAB= 28°

Now, each angle of rectangle is a right∠.

So, ∠A= 90°

=) ∠OBC+ ∠OAB= 90°

=) ∠OBC+ 28° =90°

=) ∠OBC= (90-28)°

=) ∠OBC= 62°

Hope it helps ☺️