Question

The diagonals of a rectangle ABCD intersect at O. if BOC=70 find anglesODA

Answer 1

Given; /_ BOC = 70°

Since the diagonal are the same and the bisector of each other.

Thus in ∆BOC;

• BO=CO
• => /_OBC = /_OCB = a ( suppose )

Therefore by angle sum property in ∆BOC;

• /_OBC + /_OCB + /_ BOC = 180°
• a + a + 70° = 180°. { from given and assumed }
• 2a = 110°
• a = 55°.................(1)

Since AD || BC ( opposite sides of a rectangle are equal and parallel )

Thus by Alternate Interior Angles ;

• /_ODA = /_OBC
• /_ODA = a ( as /_ OBC = a ; assumed )
• /_ODA = 55° (from 1)

Therefore /_ODA = 55°

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