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In a parallelogram ABCD, the diagonals bisect each other at $O$ . If $∠ A B C = 30 °, ∠ B D C = 10 °$ and $∠ C A B = 70 ° .$ Find $∠ AOD .$

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answer is B.

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Detailed Solution

Opposite sides of parallelogram are equal and parallel
Question Image

∠ A B C = 30 ° ∠ A B C = ∠ A D C = 30 ° (opposite angle are equal in parallelogram)

Δ A B C ∠ C A B + ∠ A B C + ∠ B C A = 180 ° (sum of all angle of triangle is 180) 70 + 30 + ∠ B C A = 180 ° ∠ B C A = 180 ° − 100 ° ∠ B C A = 80 ° ∠ D A B = ∠ D A C + ∠ C A B ∠ D A B = 70 + 80 ∠ D A B = 150 °

So, the measure of

∠ AOD = 80 ° .

Hence, the correct option is 2.

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