Question

The diagonals of a rectangle ABCD intersect at O. If angle BOC is 44 degrees, find angle OAD

Answer 1

Step-by-step explanation:

We have

∠BOC+∠BOA=180

o

[Linear pairs]

⇒44

o

+∠BOA=180

o

⇒∠BOA=136

o

Since diagonals of a rectangle are equal and they bisect each other.

Therefore, in ΔOAB, We have

OA=OB

⇒∠1=∠2[∴ Angle opp. to equal sides are equal]

In ΔOAB, we have

∠1+∠2+∠BOA=180

o

⇒2∠1+136

o

=180

o

⇒2∠1=44

o

⇒∠1=22

o

Since each angles of a rectangle is a right angle.

∠BAD=90

o

⇒∠1+∠3=90

o

⇒22

o

+∠3=90

o

⇒∠3=68

o

Hence, ∠OAD=68

o