Question

21) In a rectangle ABCD, AC and BD intersect at O.
If angle BOC = 40° find angle OBCand angle
OCB. please answer​

Answer 1

Question: In a rectangle ABCD, AC and BD intersect at O. If angle BOC = 40° find angle OBCand angle OCB.

Given: ABCD is a rectangle ABCD, AC and BD intersect at O. Angle BOC = 40°

To find: Angle OBC and angle

OCB.

Solution:

The diagonals of rectangle are congruent and they bisect each other, therefore:

AO = OC = BO = OD

Then triangle BOC is an Isosceles triangle thus:

∠OBC = ∠OCB

And since the angles of a triangle add to 180° we can calculate angle ∠OBC as follow:

∠OBC = (180 - 40°)/2

= 140°/2

= 70° = ∠OCB

$\therefore$∠OBC = 70° = ∠OCB