Question

7. In the adjoining figure, the diagonals AC and BD of parallelogram
ABCD intersect at 0. If ZOBC = 369, ZODC = 28º and ZAOD = 64°,
find the measure of (i) ZOAD (ii) ZOCD.​

Answer 1

Answer:

In given figure,

Quadrilateral ABCD is a parallelogram.

So, AD ∣∣ BC

∴ ∠DAC = ∠ACB --- ( Alternate angle)

∴ ∠ACB = 32

∘

∠AOB + ∠BOC = 180

∘

--- (straight angle)

⇒70

∘

+ ∠BOC = 180

∘

∴ ∠BOC = 110

∘

In △BOC,

∠OBC + ∠BOC + ∠OCB = 180

∘

⇒∠OBC + 110

∘

+ 32

∘

= 180

∘

⇒ ∠OBC = 38

∘

∴ ∠DBC = 38

∘