ABCD is a parallelogram in which - DAO - 40- BAO - 35- and - COD- 65- - Find - ODC-

∠ AOB = ∠ COD = 65^∘ [Vertically Opposite Angles] In Δ AOB, ∠ OAB + ∠ AOB + ∠ ABO = 180^∘ ⇒ 35^∘+ 65^∘+ ∠ OBA = 180^∘ ⇒∠ OBA = 80^∘ ∠ ODC = ∠ OBA =80^∘ [Alter ...

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Standard VIII

Mathematics

Angle Sum Property of a Polygon

ABCD is a par...

Question

ABCD is a parallelogram in which $∠ D A O = 40^{\circ}$ , $∠ B A O = 35^{\circ} a n d ∠ C O D = 65^{\circ}$ . Find $∠ O D C$ .

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Solution

$∠ A O B = ∠ C O D = 65^{\circ}$ [Vertically Opposite Angles]
In $Δ A O B, ∠ O A B + ∠ A O B + ∠ A B O = 180^{\circ}$
$\Rightarrow 35^{\circ} + 65^{\circ} + ∠ O B A = 180^{\circ}$
$\Rightarrow ∠ O B A = 80^{\circ}$
$∠ O D C = ∠ O B A = 80^{\circ}$ [Alternate interior angles as DC $∥$ AB.]

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ABCD is a parallelogram in which ∠DAO=40∘,∠BAO=35∘ and ∠COD=65∘ . Find ∠ODC.

∠AOB=∠COD=65∘ [Vertically Opposite Angles] In ΔAOB,∠OAB+∠AOB+∠ABO=180∘ ⇒35∘+65∘+∠OBA=180∘ ⇒∠OBA=80∘ ∠ODC=∠OBA=80∘ [Alternate interior angles as DC ∥ AB.]

ABCD is a parallelogram in which $∠ D A O = 40^{\circ}$ , $∠ B A O = 35^{\circ} a n d ∠ C O D = 65^{\circ}$ . Find $∠ O D C$ .