Question

the diagonals of a rectangle ABCD intersect at O. if angle AOB is 114°, find angle ACD and angle ADB.

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Answer 1

Answer:

Since, diagonals of rectangle are equal and bisect each other so

AC = BD

1 AC / 2 = 1 BC / 2

OC = OD

Therefore, COD is isosceles triangle

Hence, < OCD = < ODC

< COD = 114° [ Vertically opposite angle ]

< COD + < OCD + < ODC = 180° [ Angle sum pro. ]

Let < OCD = x°

x° + x° = 180° - 114°

2x = 66°

x = 33°

Hence, < ODC = < OCD or < ACD = 33°

Since, AB || CD where BD is transversal.

< ODC = < ABO or < ABD [ Alternate angle ]

< ABD = 33°

Step-by-step explanation:

Answer 2

see above attachment...