the diagonals of a rectangle ABCD meet at O. IF angle BOC = 44, find angle OAD.

 angle BOC = angle AOD = 44 degree ( vertically opposite angles)

diagonal AC= diagonal BD

or, 1/2 AC = 1/2 BD

or, OA = OD ( diagonals of a rectangle bisect each other.

In triangle AOD,

OA = OD

Therefore, it is an isosceles triangle.

angle OAD = angle ODA ( angles opposite to equal sides are equal )

Now, angle AOD + angle OAD + angle ODA = 180 degree ( sum of the angles of a triangle measures 1800 degree)

or, angle AOD + 2( angle OAD ) = 180 degree ( angle OAD= angle ODA)

or, 40 degree + 2( angle OAD) = 180 degree

or, 2 ( angle OAD) = 140 degree

or, angle OAD= 70 degree

ANSWER= angle OAD = 70 degree.

angle BOC = angle AOD = 44 degree ( vertically opposite angles)

diagonal AC= diagonal BD

or, 1/2 AC = 1/2 BD

or, OA = OD ( diagonals of a rectangle bisect each other.

In triangle AOD,

OA = OD

Therefore, it is an isosceles triangle.

angle OAD = angle ODA ( angles opposite to equal sides are equal )

Now, angle AOD + angle OAD + angle ODA = 180 degree ( sum of the angles of a triangle measures 1800 degree)

or, angle AOD + 2( angle OAD ) = 180 degree ( angle OAD= angle ODA)

or, 44 degree + 2( angle OAD) = 180 degree

or, 2 ( angle OAD) = 136 degree

or, angle OAD= 68 degree

ANSWER= angle OAD = 68 degree.