Question

The diagonals of a rectangle ABCD intersect at O. If angle AOD=50°, find angle OCD

Answer 1

Answer:

=57°

Step-by-step explanation:

we know that, Diagonal of rectangle are equal and bisect to each other

AC=DB

½AC=½DB

AO=BO

ang OAB=OBA

In triangle AOB

Let ang OAB=OBA=x

x+114+x=180°

or 2x=180-114

or 2x=66

x=66/2

x=33

we know that opposite side of rectangle are parallel to each other

ang OAB= ang ACD. (alternate angle)

ACD=33

BOC=180-114=66°

ACB=90-33=57

CBO=180-66+57

CBO=180-123

CBO=57

AB Parallel DC

CBO= ADB=57° ans

Answer 2

Correct Question :-

The diagonals of a rectangle ABCD intersect at O. If angle AOD=50°, find angle OCD .

Answer :-

we know that , diagonal of rectangle are equal are bisect to each other

AC = BD

½AC = ½BD

AO = BO

∠OAB = ∠OBA

In ∆AOB ,

OAB = OBA = x

$x + 114 + x = 180$

$2x = 180 - 114$

$2x = 66$

$x = \frac{66}{2}$

$x = 33$

∠OAB = ∠ACD . [ Alternate angle ]

ACD = 33°

$BOC \: = 180 - 114$

$BOC = 66$

$ACB = 90 - 33 = 57$

$CBO = 180 - 66 + 57 = 171$

AB//BC

CBO = ADB = 171°

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