The opposite sides of a quadrilateral are parallel. If one angle of the quadrilateral is $60 °$ . The other angles are:

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∠ A D C = 50 °, ∠ B A D = 20 °, ∠ B C D = 120 °

∠ A D C = 60 °, ∠ B A D = 120 °, ∠ B C D = 120 °

∠ A D C = 10 °, ∠ B A D = 150 °, ∠ B C D = 120 °

∠ A D C = 70 °, ∠ B A D = 50 °, ∠ B C D = 120 °

answer is B.

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Detailed Solution

Given opposite sides of a quadrilateral are parallel and one angle of the quadrilateral is

60 °

Using adjacent angle theorem,

∠ A B C + ∠ B C D = 180 ° ⇒ ∠ B C D = 180 ° − ∠ A B C

⇒ ∠ B C D = 180 ° − 60 °

⇒ ∠ B C D = 120 °

---(i)
Now, using opposite angle theorem,

∠ B A D = ∠ B C D ° ⇒ ∠ B A D = 120 °

Also,

∠ A D C

is opposite to

∠ A B C

⇒ ∠ A D C = ∠ A B C ⇒ ∠ A D C = 60 °

The angles are

∠ A D C = 60 °, ∠ B A D = 120 °, ∠ B C D = 120 °

.
Hence, option 2 is correct.

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