Question

In a parallelogram ABCD,diagonals intersect at O.If angle AOB=100 degree,angle DBC=35 degrees,find the measure of angle AOD,angle BDA,and angle DAC

Answer 1

Answer:

Here angle AOD = 80 degree

BDA = 35 degree

DAC = 65 degree

Step-by-step explanation:

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Answer 2

Answer :

• ∠AOD = 80°

• ∠BDA = 35°

• ∠DAC = 65°

Explanation :

Given :

• In a parallelogram ABCD,diagonals intersect at O

• ∠AOB = 100°

• ∠DBC = 35°

To Find :

• ∠AOD

• ∠BDA

• ∠DAC

Solution :

∠BOA + ∠AOD = 180°

⇒ 100° + ∠AOD = 180°       [liner pair axiom]

⇒ ∠AOD = 180° - 100°

∴ ∠AOD = 80°

We know ∠DBC = 35°

∴ ∠BDA = 35°            [Alternate interior angles are congruent]

Now we know ∠AOD and ∠BDA

Therefore,

∠AOD + ∠BDA + ∠DAC = 180°         [Angle sum property]

⇒ 80° + 35° + ∠DAC = 180°

⇒ 115 + ∠DAC = 180°

⇒ ∠DAC = 180 - 115

∴ ∠DAC = 65