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

angle BOC = angle AOD ( V. O. A )

AC = BD ( diagonals of rectangle are equal )

=> 1/2 of AC = 1/2 of BD

=> AO = DO

so AOD is an isosceles triangle.

Now, in triangle AOD,

ANGLE OAD +ODA+ AOD =180 degree

=> 2OAD + 44 = 180

=> 2OAD = 180 - 44

• 36

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

• 3

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